Solving Systems of Equations Word Problems Review
Name:_______KEY____________
Writing Systems of Equations Given Word Problems
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
T = 26
B) T + C = 118
T + 26 = C
C) T + C = 64
T – C = 26
D) T + C = 118
T = C + 26
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
4t + 3m = 1500
C) 50 + 4t = 1500
30 + 3m = 138
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
6t + 4b = 188
B) 4t = 38
6b = 188
C)
D)
t + b = 188
6t + 4b = 38
t + b = 38
4t + 6b = 188
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
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
B) 50t + 4m = 1500
30t + 3m = 138
D) 50t + 30m = 1500
4t + 3m = 138
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
L = 5 – 4W
B) 2L + 2W = 90
L = 4W – 5
C) L + W = 90
L = 5W – 4
D) L + W = 90
W = 5 – 4L
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
a+c=3
B) a + c = 8
3a + 5c = 30
C) 5a + 3c = 8
a + c = 30
D) 5a + 3c = 30
a+c=8
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
g = 2b + 3
C) g + b = 24
g = 2b – 3
B) g + b = 24
b = 2g + 3
D) g + b = 24
b = 3 – 2g
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
0.25q + 0.10d = 6.80
B) d = 3 + q
q + d = 6.80
C) d = 3q
0.25q + 0.10d = 6.80
D) q = 3d
q + d = 6.80
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
349x + 469y = 17,516
C) 349x + 469y = 44
x + y = 17,516
B)
x + y = 44
19x + 25y = 17,516
D) 19x + 25y = 44
349x + 469y = 17,516
E) None of the above.
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)
B)
C)
D)
E)
2 adult tickets
3 adult tickets
4 adult tickets
5 adult tickets
None of the above
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)
B)
C)
D)
E)
$7 popcorn and $4 cotton candy
$4 popcorn and $7 cotton candy
$6 popcorn and $2 cotton candy
$4 popcorn and $9 cotton candy.
None of the above
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?
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) 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.
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
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?
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) $1.98
B) $2.50
C) $0.86
D) 1.35
E) None of the above
A) 80 pizzas and 25 sodas
B) 25 pizzas and 80 sodas
C) 27 pizzas and 76 sodas
D) 76 pizzas and 27 sodas
E) None of the above
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?
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)
B)
C)
D)
E)
A) 16 baskets
B) 4 baskets
C) 12 baskets
D) 8 baskets
E) None of the above
11 rings & 12 bracelets
12 rings & 7 bracelets
10 rings & 9 bracelets
12 bracelets & 7 rings
None of the above