solving systems of equations word problems review...

Writing Systems of Equations Given Word Problems

Solving Systems of Equations Word Problems Review

Name:_______KEY____________

2. A television weighs 50 pounds and a microwave weighs 30

pounds. A TV occupies 4 cubic feet and microwave occupies 3

cubic feet. A truck is carrying 1500 pounds of cargo that occupies

138 cubic feet of space. Which system of equations can be used

to find the total number of televisions, t, and microwaves, m, that

are in the truck?

A) 50t + 30m = 138 B) 50t + 4m = 1500

4t + 3m = 1500 30t + 3m = 138

C) 50 + 4t = 1500 D) 50t + 30m = 1500

30 + 3m = 138 4t + 3m = 138

7. Mr. Newman bought 8 tickets to a chili supper

and spent a total of $30. He bought a combination

of adult tickets for $5 each and child tickets $3 each.

Which system of equations below will determine the

number of child tickets, c, and the number of adult

tickets, a, he bought?

A) 8a + 5c = 30 B) a + c = 8

a + c = 3 3a + 5c = 30

C) 5a + 3c = 8 D) 5a + 3c = 30

a + c = 30 a + c = 8

5. Ricki has a prepaid

cellphone. Last week Ricki

made 4 calls and sent 20 text

messages which cost him $4.

This week he made 10 calls

and sent 5 text messages

which cost him $5.50. Write

a system describing the

number of calls, c, and the

number of text messages, t,

that Ricki made over the past

two weeks.

4c + 20t = 4

10c + 5t = 5.5

4. The perimeter of a rectangular wooden deck is 90

sq ft. The deck’s length is 5 feet less than 4 times its

width. Which system of linear equations can be used

to determine the length, L, and width, W, of the

wooden deck?

A) 2L + 2W = 90 B) 2L + 2W = 90

L = 5 – 4W L = 4W – 5

C) L + W = 90 D) L + W = 90

L = 5W – 4 W = 5 – 4L

1. The sum of Teresa’s and Cathy’s weight is

118 pounds. Teresa weighs 26 pounds more

than Cathy. If Teresa’s weight is T and Cathy’s

weight is C, which of these systems of

equations best represents this relationship?

A) T + C = 118 B) T + C = 118

T = 26 T + 26 = C

C) T + C = 64 D) T + C = 118

T – C = 26 T = C + 26

3. The Country Buffet restaurant has tables that seat 6

people and booths that can seat 4 people. The restaurant

has 38 seating units for seating a total of 188 people.

Which system of equations could you use to find the

number of tables, t, and the number of booths, b, that are at

the restaurant?

A) t + b = 38 B) 4t = 38

6t + 4b = 188 6b = 188

C) t + b = 188 D) t + b = 38

6t + 4b = 38 4t + 6b = 188

6. A group of 28 people

attended the fieldtrip. The

number of teachers on the

fieldtrip was 20 less than

the number of students.

Write a system of equations

that describes the number

of teachers, t, and the

number of students, s, that

went on the fieldtrip.

t = s – 20

t + s = 28

Solve Systems of Equations Given Word Problems

1. Jose bought 9 movie tickets for a total of $54.

Adult tickets cost $8 each and child tickets cost $3.50

each. How many adult tickets did he buy?

A) 2 adult tickets

B) 3 adult tickets

C) 4 adult tickets

D) 5 adult tickets

E) None of the above

8. A total of 24 students are in Alfred’s class. The

number of girls in the class is 3 more than twice the

number of boys. Which system of equations can be

used to find g, the number of girls who are in Alfred’s

class, and b, the number of boys?

A) g + b = 24 B) g + b = 24

g = 2b + 3 b = 2g + 3

C) g + b = 24 D) g + b = 24

g = 2b – 3 b = 3 – 2g

2. Sarah and James are selling popcorn and cotton candy at

the State Fair. Sarah sold 3 bags of popcorn and 9 sticks of

cotton candy for a total of $75. James sold 8 bags of

popcorn and 5 sticks of cotton candy for a total of $67.

Which is cost of the popcorn and stick of cotton candy?

A) $7 popcorn and $4 cotton candy

B) $4 popcorn and $7 cotton candy

C) $6 popcorn and $2 cotton candy

D) $4 popcorn and $9 cotton candy.


10. An electronics store advertised a 19-inch model TV for $349 and a 25-inch model TV for $469. During one

month they sold 44 TVs total and profited an amount of $17,516. If x represents the number of 19-inch TVs and y

represents the number of 25-inch TVs, which system of equation best describes this situation?

A) x + y = 44 B) x + y = 44

349x + 469y = 17,516 19x + 25y = 17,516

C) 349x + 469y = 44 D) 19x + 25y = 44

x + y = 17,516 349x + 469y = 17,516

E) None of the above.

9. Ted has $6.80 in quarters and dimes. The number of

dimes is 3 times the number of quarters. Which system of

equations can be used to find q, the number of quarters, and

d, the number of dimes, that Ted has?

A) q = 3 + d B) d = 3 + q

0.25q + 0.10d = 6.80 q + d = 6.80

C) d = 3q D) q = 3d

0.25q + 0.10d = 6.80 q + d = 6.80

3. A group of 48 senior citizens attended a baseball

game. The number of women in attendance was 12

more than the number of men. How many men and

women attended the baseball game?

A) 20 men and 28 women

B) 28 men and 20 women

C) 30 men and 18 women

D) 18 men and 30 women

E) None of the above.

5. Two burgers and one hotdog cost $4.82. At the

same price, one burger and two hotdogs cost $3.70.

How much does a hotdog cost?

A) $1.98

B) $2.50

C) $0.86

D) 1.35


4. Kathy and Brian drove a total of 750 miles in 12

hours. Kathy drove the first part of the trip at 65 miles

per hour and Brian drove the remaining part of the trip

at 55 miles per hour. For what length of the time did

Kathy and Brian drive?

A) Kathy drove 3 hours and Brian drove 9 hours

B) Kathy drove 9 hours and Brian drove 3 hours

C) Kathy drove 6 hours and Brian drove 6 hours

D) Kathy drove 8 hours and Brian drove 4 hours


6. At the football game they sold $4 pizzas and $2

sodas, which made the school $260. The number of

sodas sold was 5 more than three times the number of

pizzas sold. Determine the amount of pizza and sodas

sold.

A) 80 pizzas and 25 sodas

B) 25 pizzas and 80 sodas

C) 27 pizzas and 76 sodas

D) 76 pizzas and 27 sodas


7. Charlie went to Juarez, Mexico, on a shopping trip.

He bought silver rings at $5 each and bracelets at $8

each. If he bought a total of 19 items and spent $131,

how many bracelets and rings did he buy?

A) 11 rings & 12 bracelets

B) 12 rings & 7 bracelets

C) 10 rings & 9 bracelets

D) 12 bracelets & 7 rings


8. In a basketball game Jane and Francine made 20

baskets. Jane scored 4 times as many baskets as Francine.

How many baskets did Jane score?

A) 16 baskets

B) 4 baskets

C) 12 baskets

D) 8 baskets


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