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WorksheetsUnit 6 Test Review
Total questions: 40
Worksheet time: 5hrs 34mins
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
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
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
The little bunny ate 20 carrots and he could eat another 5 carrots per day. The big bunny had already eaten 60 carrots and he could eat 25 more carrots per day. Write a system of equations for this situation.
y = 5x + 20
y = 25x + 60
y = 20x + 5
y = 60x + 25
y = 60x + 5
y = 20x + 25
y = 5x + 60
y = 25x + 20
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
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
Match an equation with the sentence:
A total of 17 cats and dogs went to the beach
C + D = 17
C − D = 17
CD = 17
C + 17= D
Match a sentence with this equation:
2B + 3F = 22.50
Joe bought 2 burgers and 3 fries for $22.50
Mary bought 3 burgers and 2 fries for 22.50
Norman ate 2 burgers and gave away 3 fries in 22.50 minutes
Ivy bought 2 burgers and 3 fries for 2.20
Match a sentence with this equation: C = 7.50p + 3.00
JB's Deli charges $ 0.75 for each pizza and $3.00 per topping
Sally's Pizza charges $3.00 per pizza with a $7.50 delivery fee
Pizza Time charges $7.50 for each pizza and $.30 for the delivery fee
Pizza Planet charges $7.50 per pizza with a $3.00 delivery fee
Tania had 35 coins in pennies and nickels. She had $1.03. Which system of equations could be used to determine the number of coins she has?
.01p + .05n = 35
p + n = 103
1p + 5n = 1.03
p + n = 35
.01p + .05n = 1.03
p + n = 35
.05p + .01n = 1.03
p + n = 35
The perimeter of a rectangle is forty inches. The length is two inches more than three times the width.
2L + 2w = 40
L = 3w + 2
2L + 2w = 40
w = 3L + 2
2L + 2w = 40
L = 2w + 3
2L + 2w = 40
w = 2L + 3
The perimeter of a rectangle is 44 units. If the length is 2 units longer than the width, what are the dimensions of the rectangle?
22 X 20
20 X 18
12 X 10
8 X 6
Solve:
x + y = 55
x - y = 3
Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?
Sugar Cookies $5
Oatmeal Cookies $3
Sugar Cookies $4
Oatmeal Cookies $8
Sugar Cookies $2
Oatmeal Cookies $6
Sugar Cookies $3
Oatmeal Cookies $6
Today, the average temperature in Texas is 35 degrees and is expected to rise 3 degrees per day. It’s an average of 72 degrees in North Carolina and expected to fall 2 degrees every day. When will they reach the same temperature?
37 days
146 days
7.4 days
57.2 days
John’s age is Ann’s Age decreased by 7. The sum of their ages is 45. Find John’s age.
45 years old
26 years old
7 Years old
19 years old
What is the solution to the system of equations?
No Solution
(2, 0)
Infinitely Many Solutions
(0, 2)
What is the solution of the system of equations shown in the graph?
(-1, -2)
(-2, -1)
(0, 1)
There is no solution.
Child $5
Child $6
Child $16
Child $13
Oatmeal Cookies $3
Oatmeal Cookies $8
Oatmeal Cookies $6
Oatmeal Cookies $6
The sum of Mrs. LaRoque's and Mrs. Murphy's ages is 61. The difference is 7. What are their ages?
31 and 31
54 and 7
27 and 34
21 and 40
Solve the system of inequalities by graphing.
Which of the following is a solution to the systems of inequalities?
(0, 0)
(-3, 0)
(2, -5)
(3, -1)
Which point is a solution?
(0, 6)
(-3, 5)
(1, 0)
(-4, 3)
Write the system of inequalities.
Carlos works at a movie theater selling tickets. The theater has at most 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.
x + y ≤ 300
7.5x + 5.5y ≥ 2000
x + y < 300
7.5x + 5.5y ≥ 2000
x + y ≤ 300
7.5x + 5.5y ≤ 2000
x + y > 2000
7.5x + 5.5y ≤ 300
Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?
2x + 3y > 100
x + y ≤ 40
100x + 2y > 3
x + y ≤ 40
100x + 40y > 100
3x + 2y ≤ 40
3x + 2y > 100
x + y ≤ 40
3b + 6t > 66
3b + 6t < 66
b + t < 66
b + t < 66
The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?
A vending machine has nickels and dimes. The vending machine has 32 coins in total, with a value of $2.60. What equation models the scenario?
n + d = 32
.05n + .10d = 2.60
n + d = 2.60
.05n + .10d = 32
n + d = 32
.10n + .25d = 2.60
n + d = 2.60
.10n + .25d = 32
A piggy bank has dimes and quarters. The piggy bank has 25 coins, and has a value of $4.90. What system of equations models this scenario?
d + q = 25
.10d + .25q = 4.90
d + q = 4.90
.10d + .25q = 25
d + q = 25
.05d + .10q = 4.90
d + q = 4.90
.05d + .10q = 25
Little Timmy has saved coins in his piggy bank. He has 40 dimes and nickels worth $3.35.
n+d=3.35
0.05n+0.10d=40
n+d=40
0.05n+0.10d=3.35
n+d=40
5n+10d=3.35
n+d=40
0.10n+0.05d=3.35
