Free Printable Writing Equations for Word Problems

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Writing Equations for Word Problems

Total questions: 25

Worksheet time: 5hrs 53mins

Name

Class

Date

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

x + y = 33
y = 2x - 3

x + y = 33
x = 2y - 3

x + y = 33
x = 3 - 2y

x + y = 3
x = 33 - 2y

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

4x + 6y = 3
13.5x - 13y = 6

x + y = 4
x - y = 6

4x + 6y = 13
3x + 7y = 13.5

4x - 6y = 13
3x - 7y = 13.5

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?

x - y = -10
x + y = -2

x = -2
y = 5

x + y = -2
x - y = -10

x + y = -10
x - y = -2

The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3. Which system of equations represents the situation?

2x + 3y = 55
2x + 5y = 3

x + y = 55
x - y = 3

x + y = 3
x - y = 55

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

S + A = 530

3S + 4A = 1740

S + A = 530

4S + 3A = 1740

S + A = 1740

3S + 4A = 530

S + A = 1740

4S + 3A = 530

1. The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

5q + 2z = 1.32
1z = 0.75

5q + 2z = 1.32
3q + 1z = 0.75

q + z = 1.32
q + z = 0.75

5q + 2z = 0.75
3q + 1z = 1.32

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

y = 9.65 + x

y = 8.40 + x

y = 9.65x + 43

y = 8.40x + 58

y =9.65x

y = 8.40x

y = 9.65x - 43

y = 8.40x - 58

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

10c + 5d = 14.25
5c + 10d = 16.50

10c + 5d = 16.50
5c + 10d = 14.25

c + d = 10
5c + 10d = 16.50

c + d = 5
5c + 10d = 16.50

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation?

x + y = 6
14.80x + 17y = 91

x + y = 91
14.80x + 17y = 6

x + y = 6
14.80y + 17x = 91

x + y = 91
14.80x+ 17y = 6

10.

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.

Which system best represents the situation?

4x + 7y = 578

x + y = 3365

4x + 7y = 3365

x + y = 578

4y + 7x = 578

x + y = 3365

4y + 7x = 3365

x + y = 578

11.

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

1s + 3c = 38

2s + 3c = 52

3s + 1c = 38

3s + 2c = 52

s + c = 38

s + c = 52

3s + 3c = 38

1s + 2c = 52

12.

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

x + y = 1550

y = 4x

x + y = 1550

y = x + 4

y - x = 1550

y = 4x

y = 1550 + x

y = x + 4

13.

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

d + n = 6.60

.10d + .05n = 80

d + n = 80

d + n = 6.60

d + n = 80

.10d + .05n = 6.60

d + n = 80

.05d + .10n = 6.60

14.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping.The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

y = 6.80 + .65x

y=7.30+.90x

x + y = 6.80

x + y = 7.30

y = 6.80+.90x

y = 7.30 + .65x

y + .90x = 6.80

y + .65x = 7.30

15.

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

t: # of tacos
m: # of glasses of milk

t: Cost of each taco
m: Cost of each glass of milk

t: total cost
m: # of food items

t: Cost of each glass of milk
m: Cost of each taco

16.

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

t + n = 54

t = 3n + 8

t + n = 54

n = 3t + 8

t + n = 54

t = 3n - 8

t + n = 8

t = 3n + 54

17.

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.

h = 2C + 15

C = 15h + 2

h = 15C + 2

C = 2h + 15

18.

Margaret is a waitress at The Seafood Bonanza. She earns $3 an hour plus 90% of her tips. Write an equation for her salary, S, if she works h hours and earns d dollars in tips.

3h + 0.90d = S

S = 90d + 3h

S = 3d + 90h

S = 3h + 9.0d

19.

At Joe's Clown Car Rental Agency, renting a car costs $35 plus $0.75 for every mile it is driven. What is an equation that can be used to find the number of miles, m, a vehicle was driven, if the total rental charge was $222.50?

222.5 = m(35 + 0.75)

222.5 = 35 + 0.75m

222.5 = 0.75 + 35m

222.5 = 0.75(m + 35)

20.

Lisa went to the mall to do her back-to-school shopping. When she returned, she noticed that the number of shirts (s) she purchased was 3 more than twice the number of pants (p) she bought. What is an equation that can be used to represent the number of shirts Lisa purchased?

p=3 + 2s

s + 2p =3

s = 3 + 2p

2p = s + 3

21.

Norb is a waiter in a diner. He earns $4 per hour plus 95% of his tips. Which equation can be used to determine his salary, S, if he works t hours and earn d dollars in tips?

S = 4t + 0.95d

S = 95t + 4d

S = 0.4t + 9.5d

S = 4t + 9.5d

22.

A rental company at Best Bargain Rental costs $150 a week, plus $0.10 per mile. Which equation represents the relationship between the number of miles (x) and the total cost in dollars (y) for a 2- week period?

y = 2(150)(0.10x)

y = 2(150) + 0.10x

y = 150 + 2(0.10x)

y = 2(150 + 0.10x)

23.

Bob's Plumbing charges $15 per hour plus a service fee of $40 for coming out to your house. Which equation models this situation?

y = 15x + 40

y = 40x + 15

y = 15x

y = 15x - 40

24.

Dexter's Gym charges a one-time registration fee of $40 and $20 each month. The total fee after x months is $340. Which equation models this situation?

40x + 20 = 340

20x + 40 = 340

20x - 40 = 340

20 + 340 = 40x

25.

Scott's Automotive charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie was charged $63.

35x + 7 = 63

7x = 63

7x - 35 = 63

7x + 35 = 63

100 %

Writing Equations for Word Problems

Total questions: 25

Worksheet time: 5hrs 53mins

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