The School Art Club Wants to Raise No More Than 750 in Ticket Sales

Math Models

xxx Solve Applications with Linear Inequalities

Learning Objectives

By the end of this section, you lot will be able to:

• Solve applications with linear inequalities

Before you get started, take this readiness quiz.

1. Write every bit an inequality: x is at least xxx.
   If you missed this problem, review (Figure).
2. Solve
   If you missed this problem, review (Figure).

Solve Applications with Linear Inequalities

Many existent-life situations require usa to solve inequalities. In fact, inequality applications are so common that we ofttimes do not fifty-fifty realize we are doing algebra. For case, how many gallons of gas can be put in the auto for ?xx? Is the rent on an apartment affordable? Is there plenty fourth dimension before course to go get lunch, consume information technology, and return? How much money should each family unit member's holiday gift cost without going over budget?

The method we will use to solve applications with linear inequalities is very much similar the one we used when we solved applications with equations. We will read the problem and make sure all the words are understood. Next, we will identify what nosotros are looking for and assign a variable to represent it. We will restate the problem in one sentence to arrive like shooting fish in a barrel to translate into an inequality. Then, we will solve the inequality.

Emma got a new task and will accept to move. Her monthly income will be ?5,265. To qualify to rent an apartment, Emma's monthly income must exist at least three times every bit much equally the rent. What is the highest hire Emma volition qualify for?

Alan is loading a pallet with boxes that each weighs 45 pounds. The pallet tin can safely support no more than than 900 pounds. How many boxes can he safely load onto the pallet?

There can be no more than than 20 boxes.

The elevator in Yehire's apartment building has a sign that says the maximum weight is ii,100 pounds. If the average weight of one person is 150 pounds, how many people can safely ride the lift?

A maximum of 14 people can safely ride in the elevator.

Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is non a whole number. In that example, we must circular the algebraic solution to a whole number. The context of the application will determine whether we circular upwardly or downwardly. To bank check applications like this, nosotros will round our answer to a number that is like shooting fish in a barrel to compute with and make certain that number makes the inequality truthful.

Dawn won a mini-grant of ?4,000 to buy tablet computers for her classroom. The tablets she would similar to buy cost ?254.12 each, including revenue enhancement and delivery. What is the maximum number of tablets Dawn tin can buy?

Angie has ?20 to spend on juice boxes for her son'southward preschool picnic. Each pack of juice boxes costs ?2.63. What is the maximum number of packs she can buy?

vii packs

Daniel wants to surprise his girlfriend with a birthday party at her favorite eating house. It will cost ?42.75 per person for dinner, including tip and tax. His budget for the political party is ?500. What is the maximum number of people Daniel can have at the party?

11 people

Pete works at a computer shop. His weekly pay will be either a fixed amount, ?925, or ?500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed corporeality of ?925?

Tiffany only graduated from higher and her new chore will pay her ?20,000 per year plus ii% of all sales. She wants to earn at least ?100,000 per year. For what total sales volition she exist able to reach her goal?

at least ?4,000,000

Christian has been offered a new job that pays ?24,000 a yr plus iii% of sales. For what full sales would this new task pay more than than his current task which pays ?60,000?

at least ?one,200,000

Sergio and Lizeth have a very tight vacation budget. They plan to rent a car from a company that charges ?75 a week plus ?0.25 a mile. How many miles tin can they travel and still keep within their ?200 budget?

Taleisha'due south telephone plan costs her ?28.lxxx a month plus ?0.20 per text message. How many text messages can she use and keep her monthly phone nib no more than than ?50?

no more than than 106 text messages

Rameen's heating pecker is ?v.42 per month plus ?ane.08 per therm. How many therms can Rameen employ if he wants his heating bill to be a maximum of ?87.50?

no more than 76 therms

A common goal of well-nigh businesses is to make a profit. Profit is the money that remains when the expenses take been subtracted from the coin earned. In the next example, we will find the number of jobs a pocket-size businessman needs to do every month in order to brand a certain amount of profit.

Elliot has a landscape maintenance business. His monthly expenses are ?ane,100. If he charges ?60 per chore, how many jobs must he do to earn a profit of at least ?4,000 a month?

Caleb has a pet sitting business organization. He charges ?32 per hr. His monthly expenses are ?2,272. How many hours must he work in lodge to earn a profit of at least ?800 per month?

at least 96 hours

Felicity has a calligraphy business. She charges ?2.fifty per wedding ceremony invitation. Her monthly expenses are ?650. How many invitations must she write to earn a profit of at least ?2,800 per month?

at least 1,380 invitations

Sometimes life gets complicated! There are many situations in which several quantities contribute to the total expense. Nosotros must make sure to business relationship for all the individual expenses when nosotros solve problems like this.

Brenda'southward best friend is having a destination wedding and the event will last 3 days. Brenda has ?500 in savings and can earn ?15 an hr babysitting. She expects to pay ?350 airfare, ?375 for food and entertainment and ?lx a dark for her share of a hotel room. How many hours must she babysit to have enough money to pay for the trip?

Malik is planning a 6-solar day summer holiday trip. He has ?840 in savings, and he earns ?45 per hr for tutoring. The trip will cost him ?525 for airfare, ?780 for food and sightseeing, and ?95 per dark for the hotel. How many hours must he tutor to have plenty money to pay for the trip?

at to the lowest degree 23 hours

Josue wants to keep a ten-day route trip next spring. It will cost him ?180 for gas, ?450 for nutrient, and ?49 per dark for a cabin. He has ?520 in savings and tin earn ?30 per driveway shoveling snow. How many driveways must he shovel to accept enough money to pay for the trip?

at least 20 driveways

Central Concepts

• Solving inequalities
  1. Read the trouble.
  2. Place what we are looking for.
  3. Name what nosotros are looking for. Choose a variable to represent that quantity.
  4. Translate. Write a sentence that gives the information to find it. Translate into an inequality.
  5. Solve the inequality.
  6. Check the respond in the trouble and brand sure it makes sense.
  7. Answer the question with a consummate judgement.

Section Exercises

Practise Makes Perfect

Solve Applications with Linear Inequalities

In the following exercises, solve.

Mona is planning her son's birthday party and has a upkeep of ?285. The Fun Zone charges ?19 per child. How many children can she have at the party and stay within her budget?

xv children

Carlos is looking at apartments with 3 of his friends. They want the monthly rent to be no more than ?2360. If the roommates split the rent evenly amidst the four of them, what is the maximum hire each will pay?

A water taxi has a maximum load of i,800 pounds. If the average weight of one person is 150 pounds, how many people can safely ride in the water taxi?

12 people

Marcela is registering for her higher classes, which cost ?105 per unit. How many units tin she take to have a maximum cost of ?1,365?

Arleen got a ?20 gift card for the coffee shop. Her favorite iced drink costs ?3.79. What is the maximum number of drinks she can buy with the gift card?

five drinks

Teegan likes to play golf. He has approaching ?lx next month for the driving range. Information technology costs him ?x.55 for a saucepan of assurance each time he goes. What is the maximum number of times he can become to the driving range next calendar month?

Joni sells kitchen aprons online for ?32.50 each. How many aprons must she sell next month if she wants to earn at least ?1,000?

31 aprons

Ryan charges his neighbors ?17.l to wash their car. How many cars must he launder next summer if his goal is to earn at to the lowest degree ?one,500?

Keshad gets paid ?2,400 per month plus half dozen% of his sales. His brother earns ?3,300 per month. For what corporeality of total sales volition Keshad's monthly pay be higher than his blood brother's monthly pay?

?15,000

Kimuyen needs to earn ?4,150 per month in club to pay all her expenses. Her chore pays her ?3,475 per month plus 4% of her full sales. What is the minimum Kimuyen's full sales must be in order for her to pay all her expenses?

Andre has been offered an entry-level job. The company offered him ?48,000 per year plus 3.five% of his total sales. Andre knows that the average pay for this task is ?62,000. What would Andre's full sales need to be for his pay to exist at to the lowest degree every bit high as the average pay for this job?

?400,000

Nataly is because ii task offers. The first job would pay her ?83,000 per year. The second would pay her ?66,500 plus xv% of her total sales. What would her total sales need to be for her salary on the 2nd offer be higher than the showtime?

Jake's h2o bill is ?24.80 per month plus ?two.20 per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake tin use if he wants his nib to be no more than ?threescore?

16 ccf

Kiyoshi's phone plan costs ?17.l per month plus ?0.15 per text message. What is the maximum number of text messages Kiyoshi can utilise so the telephone neb is no more than ?56.fifty?

Marlon's Goggle box plan costs ?49.99 per calendar month plus ?5.49 per first-run motion picture. How many outset-run movies tin can he watch if he wants to go on his monthly bill to be a maximum of ?100?

nine movies

Kellen wants to rent a banquet room in a eating place for her cousin's baby shower. The restaurant charges ?350 for the banquet room plus ?32.50 per person for tiffin. How many people can Kellen accept at the shower if she wants the maximum cost to be ?1,500?

Moshde runs a hairstyling business from her business firm. She charges ?45 for a haircut and fashion. Her monthly expenses are ?960. She wants to be able to put at least ?i,200 per month into her savings account social club to open her ain salon. How many "cut & styles" must she practise to save at least ?ane,200 per month?

48 cutting & styles

Noe installs and configures software on dwelling house computers. He charges ?125 per job. His monthly expenses are ?1,600. How many jobs must he work in society to make a profit of at least ?2,400?

Katherine is a personal chef. She charges ?115 per four-person meal. Her monthly expenses are ?3,150. How many four-person meals must she sell in order to brand a profit of at least ?i,900?

44 meals

Melissa makes necklaces and sells them online. She charges ?88 per necklace. Her monthly expenses are ?3745. How many necklaces must she sell if she wants to make a profit of at least ?i,650?

Five student government officers desire to become to the state convention. It will cost them ?110 for registration, ?375 for transportation and food, and ?42 per person for the hotel. In that location is ?450 approaching for the convention in the pupil regime savings business relationship. They can earn the rest of the money they need by having a automobile wash. If they charge ?v per car, how many cars must they wash in order to have enough money to pay for the trip?

49 cars

Cesar is planning a 4-day trip to visit his friend at a higher in another state. Information technology volition cost him ?198 for airfare, ?56 for local transportation, and ?45 per day for nutrient. He has ?189 in savings and can earn ?35 for each lawn he mows. How many lawns must he mow to have plenty coin to pay for the trip?

Alonzo works as a machine detailer. He charges ?175 per car. He is planning to motion out of his parents' house and hire his first flat. He will need to pay ?120 for application fees, ?950 for security deposit, and outset and final months' rent at ?1,140 per month. He has ?i,810 in savings. How many cars must he particular to have enough money to rent the apartment?

nine cars

Eun-Kyung works equally a tutor and earns ?60 per hour. She has ?792 in savings. She is planning an anniversary political party for her parents. She would similar to invite forty guests. The party volition cost her ?1,520 for food and drinks and ?150 for the photographer. She will too have a favor for each of the guests, and each favor volition cost ?7.l. How many hours must she tutor to take enough coin for the political party?

Everyday Math

Maximum Load on a Phase In 2014, a high schoolhouse stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical product. Ii dozen students were injured. The stage could support a maximum of 12,750 pounds. If the boilerplate weight of a pupil is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage?

91 students

Maximum Weight on a Boat In 2004, a water taxi sank in Baltimore harbor and five people drowned. The h2o taxi had a maximum chapters of 3,500 pounds (25 people with average weight 140 pounds). The boilerplate weight of the 25 people on the h2o taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?

Wedding Upkeep Adele and Walter found the perfect venue for their nuptials reception. The cost is ?9,850 for up to 100 guests, plus ?38 for each boosted invitee. How many guests can attend if Adele and Walter want the full cost to be no more than ?12,500?

169 guests

Shower Budget Penny is planning a baby shower for her daughter-in-police. The eating house charges ?950 for up to 25 guests, plus ?31.95 for each boosted guest. How many guests tin can attend if Penny wants the total cost to be no more than ?1,500?

Writing Exercises

Find your last month'south phone bill and the hourly bacon you are paid at your job. (If yous do not have a job, utilize the hourly bacon you lot would realistically be paid if y'all had a chore.) Calculate the number of hours of work it would take yous to earn at least plenty money to pay your phone nib by writing an appropriate inequality and so solving it.

Answers will vary.

Find out how many units you take left, after this term, to achieve your college goal and estimate the number of units you can accept each term in college. Calculate the number of terms it will take you to achieve your college goal by writing an appropriate inequality and so solving information technology.

Cocky Check

ⓐ Subsequently completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell you about your mastery of this section? What steps will y'all accept to ameliorate?

Affiliate 3 Review Exercises

iii.ane Using a Problem Solving Strategy

Approach Give-and-take Problems with a Positive Attitude

In the following exercises, reflect on your approach to give-and-take problems.

How has your attitude towards solving word problems changed as a upshot of working through this affiliate? Explain.

answers volition vary

Did the problem-solving strategy help you solve word problems in this chapter? Explicate.

Employ a Problem-Solving Strategy for Give-and-take Problems

In the following exercises, solve using the problem-solving strategy for discussion problems. Remember to write a consummate sentence to answer each question.

Three-fourths of the people at a concert are children. If at that place are 87 children, what is the full number of people at the concert?

116

In that location are nine saxophone players in the ring. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.

Solve Number Bug

In the following exercises, solve each number discussion problem.

The sum of a number and 3 is forty-one. Find the number.

38

Twice the difference of a number and ten is l-4. Find the number.

One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.

One number is eleven more than another. If their sum is increased by seventeen, the result is 90. Find the numbers.

One number is two more than than 4 times another. Their sum is Find the numbers.

The sum of two sequent integers is Discover the numbers.

Find iii consecutive integers whose sum is

Find three consecutive even integers whose sum is 234.

Find three consecutive odd integers whose sum is 51.

15, 17, xix

Koji has ?five,502 in his savings account. This is ?xxx less than six times the amount in his checking business relationship. How much money does Koji accept in his checking account?

three.2 Solve Pct Applications

Translate and Solve Bones Percent Equations

In the post-obit exercises, translate and solve.

What number is 67% of 250?

167.5

300% of 82 is what number?

12.5% of what number is twenty?

160

72 is 30% of what number?

What percent of 125 is 150?

120%

127.5 is what percent of 850?

Solve Per centum Applications

In the following exercises, solve.

The beak for Dino'due south lunch was ?19.45. He wanted to leave xx% of the total bill equally a tip. How much should the tip be?

?3.89

Reza was very sick and lost xv% of his original weight. He lost 27 pounds. What was his original weight?

Dolores bought a crib on sale for ?350. The sale price was 40% of the original toll. What was the original price of the crib?

?875

Jaden earns ?2,680 per month. He pays ?938 a month for rent. What pct of his monthly pay goes to rent?

Find Percent Increase and Percent Decrease

In the following exercises, solve.

Angel's got a raise in his annual bacon from ?55,400 to ?56,785. Find the percent increase.

2.five%

Rowena's monthly gasoline neb dropped from ?83.75 last calendar month to ?56.95 this month. Find the percentage decrease.

Solve Simple Interest Applications

In the following exercises, solve.

Winston deposited ?3,294 in a banking company business relationship with interest charge per unit two.half dozen%. How much interest was earned in 5 years?

?428.22

Moira borrowed ?four,500 from her grandfather to pay for her first year of college. Three years later, she repaid the ?iv,500 plus ?243 interest. What was the rate of interest?

Jaime's refrigerator loan statement said he would pay ?one,026 in involvement for a 4-year loan at 13.5%. How much did Jaime infringe to buy the refrigerator?

?1,900

In 12 years, a bond that paid half dozen.35% interest earned ?7,620 interest. What was the chief of the bail?

Solve Applications with Discount or Marking-upwards

In the post-obit exercises, detect the sale cost.

The original price of a bag was ?84. Carole bought it on auction for ?21 off.

?63

Marian wants to buy a coffee table that costs ?495. Next week the coffee table volition be on sale for ?149 off.

In the following exercises, observe ⓐ the corporeality of discount and ⓑ the sale price.

Emmett bought a pair of shoes on sale at twoscore% off from an original cost of ?138.

ⓐ ?55.20 ⓑ ?82.80

Anastasia bought a apparel on auction at 75% off from an original price of ?280.

In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percentage, if needed.)

Zack bought a printer for his role that was on sale for ?380. The original cost of the printer was ?450.

ⓐ ?70 ⓑ 15.6%

Lacey bought a pair of boots on sale for ?95. The original cost of the boots was ?200.

In the post-obit exercises, discover ⓐ the amount of the mark-upwards and ⓑ the list price.

Nga and Lauren bought a chest at a flea market place for ?fifty. They re-finished it and then added a 350% marker-upwards.

ⓐ ?175 ⓑ ?225

Carly bought bottled water for ?0.24 per canteen at the discount store. She added a 75% mark-up earlier selling them at the football game.

3.3 Solve Mixture Applications

Solve Money Give-and-take Problems

In the post-obit exercises, solve each coin word problem.

Francie has ?4.35 in dimes and quarters. The number of dimes is five more than the number of quarters. How many of each coin does she have?

16 dimes, eleven quarters

Scott has ?0.39 in pennies and nickels. The number of pennies is eight times the number of nickels. How many of each coin does he accept?

Paulette has ?140 in ?5 and ?10 bills. The number of ?10 bills is one less than twice the number of ?five bills. How many of each does she have?

6 ?5 bills, 11 ?10 bills

Lenny has ?3.69 in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he take?

Solve Ticket and Stamp Give-and-take Problems

In the following exercises, solve each ticket or stamp give-and-take problem.

A church luncheon made ?842. Adult tickets cost ?10 each and children's tickets toll ?6 each. The number of children was 12 more than than twice the number of adults. How many of each ticket were sold?

35 adults, 82 children

Tickets for a basketball game game price ?2 for students and ?5 for adults. The number of students was 3 less than x times the number of adults. The full amount of coin from ticket sales was ?619. How many of each ticket were sold?

125 tickets were sold for the jazz band concert for a total of ?ane,022. Educatee tickets price ?6 each and full general admission tickets toll ?10 each. How many of each kind of ticket were sold?

57 students, 68 adults

One afternoon the water park sold 525 tickets for a total of ?13,545. Child tickets cost ?19 each and adult tickets price ?40 each. How many of each kind of ticket were sold?

Ana spent ?4.06 buying stamps. The number of ?0.41 stamps she bought was v more than the number of ?0.26 stamps. How many of each did she buy?

3 ?0.26 stamps, viii ?0.41 stamps

Yumi spent ?34.15 ownership stamps. The number of ?0.56 stamps she bought was 10 less than iv times the number of ?0.41 stamps. How many of each did she purchase?

Solve Mixture Word Problems

In the following exercises, solve each mixture word problem.

Marquese is making x pounds of trail mix from raisins and nuts. Raisins cost ?3.45 per pound and basics price ?7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him ?vi.96 per pound?

2.two lb. of raisins, 7.eight lb. of nuts

Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will utilize basic tiles that cost ?8 per square foot and decorator tiles that cost ?20 per square foot. How many square anxiety of each tile should she employ so that the overall toll of the backsplash will be ?10 per square foot?

Shawn has ?xv,000 to invest. She will put some of information technology into a fund that pays 4.5% almanac interest and the rest in a certificate of eolith that pays 1.8% annual interest. How much should she invest in each account if she wants to earn iv.05% almanac involvement on the total amount?

?12,500 at 4.5%, ?2,500 at one.8%

Enrique borrowed ?23,500 to buy a motorcar. He pays his uncle 2% interest on the ?4,500 he borrowed from him, and he pays the depository financial institution 11.v% involvement on the rest. What average involvement rate does he pay on the total ?23,500? (Circular your answer to the nearest 10th of a percent.)

3.4 Solve Geometry Applications: Triangles, Rectangles and the Pythagorean Theorem

Solve Applications Using Triangle Backdrop

In the post-obit exercises, solve using triangle properties.

The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the third angle.

The playground at a shopping mall is a triangle with perimeter 48 feet. The lengths of 2 sides are 19 feet and 14 anxiety. How long is the 3rd side?

A triangular road sign has base xxx inches and height 40 inches. What is its surface area?

600 square inches

What is the elevation of a triangle with surface area 67.5 square meters and base 9 meters?

One angle of a triangle is more than than the smallest angle. The largest angle is the sum of the other angles. Observe the measures of all three angles.

One angle of a right triangle measures What is the measure of the other angles of the triangle?

The measure of the smallest angle in a right triangle is less than the measure of the next larger bending. Find the measures of all three angles.

The perimeter of a triangle is 97 feet. 1 side of the triangle is eleven feet more than the smallest side. The third side is half-dozen anxiety more than twice the smallest side. Find the lengths of all sides.

Use the Pythagorean Theorem

In the following exercises, utilize the Pythagorean Theorem to notice the length of the hypotenuse.

26

In the post-obit exercises, apply the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

8

8.1

In the following exercises, solve. Estimate to the nearest tenth, if necessary.

Sergio needs to attach a wire to concord the antenna to the roof of his house, as shown in the figure. The antenna is 8 feet alpine and Sergio has 10 feet of wire. How far from the base of the antenna tin he attach the wire?

Seong is building shelving in his garage. The shelves are 36 inches wide and xv inches tall. He wants to put a diagonal brace across the dorsum to stabilize the shelves, every bit shown. How long should the brace be?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The length of a rectangle is 36 feet and the width is 19 anxiety. Discover the ⓐ perimeter ⓑ expanse.

ⓐ 110 ft. ⓑ 684 sq. ft.

A sidewalk in forepart of Kathy's house is in the shape of a rectangle four feet broad past 45 anxiety long. Find the ⓐ perimeter ⓑ expanse.

The area of a rectangle is 2356 square meters. The length is 38 meters. What is the width?

62 k

The width of a rectangle is 45 centimeters. The area is 2,700 square centimeters. What is the length?

The length of a rectangle is 12 cm more than than the width. The perimeter is 74 cm. Find the length and the width.

24.v cm, 12.5 cm

The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Discover the length and the width.

3.5 Solve Compatible Motion Applications

Solve Uniform Motion Applications

In the following exercises, solve.

When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa 2 hours to bulldoze the aforementioned distance. Elsa's speed is seven miles per hour faster than Gabe'southward speed. Observe Gabe's speed and Elsa's speed.

Gabe 70 mph, Elsa 77 mph

Louellen and Tracy met at a restaurant on the route between Chicago and Nashville. Louellen had left Chicago and collection 3.2 hours towards Nashville. Tracy had left Nashville and drove iv hours towards Chicago, at a speed i mile per hour faster than Louellen's speed. The distance between Chicago and Nashville is 472 miles. Detect Louellen'southward speed and Tracy'due south speed.

2 busses leave Amarillo at the aforementioned time. The Albuquerque bus heads westward on the I-40 at a speed of 72 miles per hour, and the Oklahoma City autobus heads due east on the I-forty at a speed of 78 miles per hour. How many hours volition it take them to be 375 miles apart?

2.v hours

Kyle rowed his boat upstream for 50 minutes. It took him 30 minutes to row dorsum downstream. His speed going upstream is 2 miles per hour slower than his speed going downstream. Discover Kyle's upstream and downstream speeds.

At half dozen:30, Devon left her business firm and rode her cycle on the flat road until 7:xxx. Then she started riding uphill and rode until eight:00. She rode a total of 15 miles. Her speed on the flat road was iii miles per 60 minutes faster than her speed going uphill. Discover Devon's speed on the flat road and riding uphill.

flat route eleven mph, uphill 8 mph

Anthony drove from New York Metropolis to Baltimore, a distance of 192 miles. He left at 3:45 and had heavy traffic until 5:30. Traffic was light for the rest of the drive, and he arrived at 7:thirty. His speed in light traffic was 4 miles per hour more than twice his speed in heavy traffic. Find Anthony'south driving speed in heavy traffic and low-cal traffic.

3.six Solve Applications with Linear Inequalities

Solve Applications with Linear Inequalities

In the following exercises, solve.

Julianne has a weekly food budget of ?231 for her family. If she plans to budget the same amount for each of the 7 days of the calendar week, what is the maximum amount she tin can spend on food each twenty-four hours?

?33 per day

Rogelio paints watercolors. He got a ?100 souvenir card to the fine art supply shop and wants to apply it to buy canvases. Each canvas costs ?10.99. What is the maximum number of canvases he can buy with his gift carte?

Briana has been offered a sales job in another city. The offering was for ?42,500 plus 8% of her full sales. In guild to brand it worth the move, Briana needs to have an annual salary of at least ?66,500. What would her total sales need to be for her to move?

at to the lowest degree ?300,000

Renee's car costs her ?195 per calendar month plus ?0.09 per mile. How many miles tin can Renee drive so that her monthly auto expenses are no more ?250?

Costa is an accountant. During tax season, he charges ?125 to do a simple tax return. His expenses for ownership software, renting an role, and advertising are ?6,000. How many tax returns must he do if he wants to make a profit of at least ?8,000?

at least 112 jobs

Jenna is planning a 5-day resort vacation with three of her friends. It will cost her ?279 for airfare, ?300 for food and amusement, and ?65 per day for her share of the hotel. She has ?550 saved towards her holiday and can earn ?25 per hour as an assistant in her uncle'southward photography studio. How many hours must she work in order to have enough money for her holiday?

Practice Test

Four-fifths of the people on a hike are children. If in that location are 12 children, what is the total number of people on the hike?

15

One number is 3 more than than twice another. Their sum is Find the numbers.

The sum of two sequent odd integers is Find the numbers.

Marla's breakfast was 525 calories. This was 35% of her total calories for the mean solar day. How many calories did she have that solar day?

Humberto's hourly pay increased from ?16.25 to ?17.55. Observe the percent increase.

8%

Melinda deposited ?5,985 in a bank account with an interest charge per unit of ane.9%. How much involvement was earned in 2 years?

Dotty bought a freezer on sale for ?486.fifty. The original price of the freezer was ?695. Detect ⓐ the corporeality of discount and ⓑ the disbelieve rate.

ⓐ ?208.50 ⓑ 30%

Bonita has ?2.95 in dimes and quarters in her pocket. If she has v more dimes than quarters, how many of each coin does she have?

At a concert, ?1,600 in tickets were sold. Adult tickets were ?9 each and children's tickets were ?four each. If the number of developed tickets was 30 less than twice the number of children'southward tickets, how many of each kind were sold?

140 adult, 85 children

Kim is making viii gallons of punch from fruit juice and soda. The fruit juice costs ?6.04 per gallon and the soda costs ?4.28 per gallon. How much fruit juice and how much soda should she utilise then that the punch costs ?five.71 per gallon?

The mensurate of i angle of a triangle is twice the measure of the smallest bending. The mensurate of the third angle is fourteen more the measure of the smallest angle. Find the measures of all three angles.

What is the elevation of a triangle with surface area 277.2 foursquare inches and base 44 inches?

In the following exercises, use the Pythagorean Theorem to notice the length of the missing side. Round to the nearest tenth, if necessary.

10

A baseball diamond is really a foursquare with sides of 90 feet. How far is information technology from dwelling house plate to second base, as shown?

127.iii ft.

The length of a rectangle is two feet more than five times the width. The perimeter is xl feet. Detect the dimensions of the rectangle.

Ii planes go out Dallas at the aforementioned time. I heads east at a speed of 428 miles per hour. The other plane heads westward at a speed of 382 miles per hour. How many hours will it take them to be two,025 miles apart?

two.5 hours

Leon drove from his house in Cincinnati to his sister's business firm in Cleveland, a distance of 252 miles. It took him hours. For the first one-half hour he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic. What was his speed in heavy traffic?

Chloe has a budget of ?800 for costumes for the eighteen members of her musical theater group. What is the maximum she can spend for each costume?

at most ?44.44 per costume

Frank found a rental car deal online for ?49 per week plus ?0.24 per mile. How many miles could he bulldoze if he wants the full cost for 1 week to exist no more than than ?150?

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Source: https://opentextbc.ca/elementaryalgebraopenstax/chapter/solve-applications-with-linear-inequalities/

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