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2.5 Applications of Linear Equations - Printable Mathematics Worksheets year 12 - Wayground

2.5 Applications of Linear Equations

20 questions

12th - 12th Grade

Mathematics

2.5 Applications of Linear Equations is a Grade 12 mathematics worksheet with 20 practice questions focused on translating real-world situations into linear equations and using those equations to calculate costs and amounts. Students identify initial values and constant rates in scenarios involving gym memberships, rental fees, water levels, travel, and distance, then apply percent calculations to taxes, discounts, tips, sale prices, and total bills. The worksheet includes 19 multiple-choice questions and one fill-in-the-blank item, giving students practice distinguishing a rate from a starting value and deciding whether a problem asks for a discount, tip, tax, or final total. It is a free printable worksheet with a complete answer key, suitable for independent practice, review, or an in-class check of understanding after instruction on applications of linear equations.

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Worksheets

2.5 Applications of Linear Equations

Total questions: 20

Name
Class
Date
1.

Choose the equation that models the following situation:


Mike joins a gym for $25 up front and a $30 monthly fee.

a)

y = −25x+30y\ =\ -25x+30

b)

y=25x+30y=25x+30

c)

y=30x+25y=30x+25

d)

y=30x−25y=30x-25

2.

Choose the equation that models the following situation:


The water level in a bath tub was 14 inches and Angelo pulls the plug and it decreases at a constant rate of 2.5 inches every minute.

a)

 y = 14y\ =\ 14 

b)

 y=2.5x +14y=2.5x\ +14 

c)

 y=−2.5x−14y=-2.5x-14 

d)

 y=−2.5x+14y=-2.5x+14 

3.

Choose the equation that models the following situation:


Starting at her house, the distance Natalie is from her house if she walks to school at a constant rate of 8 feet per second.

a)

 y = 8y\ =\ 8 

b)

 y=8xy=8x 

c)

 y =x+8y\ =x+8 

d)

 y=−8xy=-8x 

4.

You are traveling to your friends house in another city that is 6 miles away. You call an UBER that charges $5 and $1.50 per mile that you travel. What is the cost of the trip?

a)

$5.00

b)

$15.00

c)

$20.00

d)

$14.00

5.
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation for C, the total cost, to rent the boat for h hours.
a)
h = 2C + 15
b)
C = 15h + 2
c)
h = 15C + 2
d)
C = 2h + 15
6.

 In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation that models this situation.

a)

y = 20x + 5

b)

y = 5x +20

7.
Easy Car Rental charges $8.50 an hour plus a rental fee of $25.50. Which equation represents the total charges for x hours?
a)
y = 8.5 + 25.5
b)
y = 25.5 + 8.5x
c)
y = 8.5 + 25.5x
8.

Daenerys bought dragon food for $29.53. If her tax was 4%, what was her total cost?

(a)  

9.

A $300 bike is on sale for 45% off. How much is the discount?

HINT: NOT THE TOTAL JUST THE DISCOUNT

a)

$145

b)

$135

c)

$200

d)

$435

10.

Mr and Mrs Smith pay their babysitter a total of $70. They decide to give a tip of 32%. How much is the tip?

HINT: NOT THE TOTAL

a)

$20

b)

$32.40

c)

$22.40

d)

$102

11.
Angela spent $30.00 at a restaurant.  If she leaves a 15% tip, how much will her TOTAL BILL be? 
a)
30.00
b)
45.25
c)
$ 34.50
d)
35.65
12.
A pair of boots are $94.99.  They are 25% off. With this discount, what is the sale price?
a)
$71.24
b)
$118.74
c)
23.7475
d)
$23.75
13.

  If you receive 25% off an item costing $22.00, how much money do you save?

HINT: NOT THE TOTAL JUST THE DISCOUNT

a)

$ 5.50

b)

$ 4.25

c)

$6.00

d)

$7.35

14.
Find the total cost.  Dinner with tax included is $23.77; you leave a 10% tip.
a)
$ 2.38
b)
$ 2.37
c)
$ 26.15
d)
$ 21.39
15.

How much tip should you leave if you want to tip 23% at Applebee's on a $27.31 bill?

HINT: NOT THE TOTAL

a)

$6.28

b)

$33.59

c)

$21.03

16.

In a video store, a DVD that sells for $15 is marked 10% off. What is the amount of discount?

HINT: NOT THE TOTAL JUST THE DISCOUNT

a)

1.00

b)

1.50

c)

16.50

d)

13.50

17.
Sales tax is __________ to the price.
a)
subtracted
b)
added
c)
multiplied
d)
divided
18.

Kaylee is buying a calculator that has a price tag of $65. At the register, the cashier applies a 15% discount to the $65 price. How much will Kaylee pay for the calculator after the 15% discount?

a)

$32.50

b)

$74.75

c)

$55.25

d)

$9.75

19.

Macy's Department Store has a 30%-off sale this week. What is the sale price for a pair of $24.00 jeans?

a)

$2.40

b)

$7.20

c)

$16.80

d)

$21.60

20.
Daniel has dinner at a restaurant and the cost of his meal is $28.00. Because of the service, he wants to leave a 20% tip. What is his total bill including tip?
a)
33.60
b)
40.00
c)
24.60
d)
30.50
Answer Key

2.5 Applications of Linear Equations

Total questions: 20

1.
c)

y=30x+25y=30x+25

2.
d)

 y=−2.5x+14y=-2.5x+14 

3.
b)

 y=8xy=8x 

4.
d)

$14.00

5.
d) C = 2h + 15
6.
b)

y = 5x +20

7.
b) y = 25.5 + 8.5x
8.
30.71
9.
b)

$135

10.
c)

$22.40

11.
c) $ 34.50
12.
a) $71.24
13.
a)

$ 5.50

14.
c) $ 26.15
15.
a)

$6.28

16.
b)

1.50

17.
b) added
18.
c)

$55.25

19.
c)

$16.80

20.
a) 33.60

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FAQs

What does the 2.5 Applications of Linear Equations worksheet cover?

This Grade 12 mathematics worksheet covers translating everyday situations into linear equations and solving related percent applications. Its 20 items use mostly multiple-choice questions, plus one fill-in-the-blank question, to practice identifying starting values and rates in models and calculating taxes, discounts, tips, sale prices, and total costs.

How can I use this worksheet to teach applications of linear equations?

Introduce the equation-modeling items by having students label the independent quantity, starting value, and rate before choosing an equation. For example, students can explain why a gym’s upfront fee is the constant term while its monthly fee is the coefficient of the number of months. After modeling, use the rental, travel, tax, discount, and tip items to connect linear relationships and percent calculations to real payment situations.

What mistakes should I watch for when students complete this worksheet?

Watch for students reversing the rate and initial value, such as writing a monthly fee as the constant term or using a positive slope when a bathtub’s water level is decreasing. In the percent items, students may calculate the discount or tip correctly but report the total bill, or subtract the wrong amount when finding a sale price. The fill-in-the-blank tax item also requires students to add the tax to the original price rather than enter only the tax.

How do I assign and grade this applications of linear equations worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key for checking the 19 multiple-choice responses and the fill-in-the-blank calculation. For printable submissions, scan student work with the Wayground for Teachers app to help grade responses efficiently.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font size or spacing so the equation choices and percent word problems are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when helpful for students working through the linear-equation models and cost calculations.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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