Test 3.2 Review
Solving Equations and Distributive Property
1. An equation is modeled below. Write
the equation and solve for the value of
y.
2. A model of an equation is shown
below. What is the value of f?
3.
4. An equation is modeled below. Write
the equation and solve for x.
5. Abby and Skyler both collect stamps.
Abby has 10 stamps and collects four
new stamps every week. Skyler has
60 stamps and collects 2 new stamps
every week. After how many weeks
will Abby and Skyler have the same
number of stamps?
The equation w + 9 = 5w + 5 is
modeled below. Which value of w
makes the equation true?
A w = -4
B w=1
C w=5
D w = 14
6. Logan and Jean Karlo are both saving
up money to buy mountain bikes.
Logan has $50 and will save $10
every week. Jean Karlo has $15 and
will save $15 every week. After how
many weeks will Logan and Jean Karlo
have the same amount of money?
7. Use the model to write the equation
and solve for the variable.
Use the scenario below to answer questions
#10-12.
Maggie and Melany own a local business
together and are about to give gifts to their
employees for the holiday season. They have
purchased small gifts for their front office
staff, and large gifts for their personal
assistants.
Hint: The shaded ones are negative
values.
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8. Draw a picture to model the equation
4x + 8 = 9x + 3 and solve for x.
Maggie purchased 4 large gifts and 2
small gifts.
Melany purchased 1 large gift and 20
small gifts.
Each small gift costs $10
Each large gift costs an equal amount
of money to each other.
10.Draw a picture to model an equation if
Melany and Maggie spent the same
amount of money.
11. How much did they spend on the
large gift item?
9. The sum of one-half a number and 7
is twice the number minus 5. Write
the equation and solve for x.
12. How much did each person spend?
13. Malcom walks 10 blocks across a field
to get to school from his house, as
show below. How many more blocks
would Malcom have to walk from his
house to school if a fence was built
around the field and he had to use the
sidewalk to walk around?
School
8 blocks
Use the table below to answer questions 17-19.
Prices listed are per person.
Company
Cost
Skis for You
$48 plus $5 an hour
Ski Right
$28 plus $15 hour
17.Your family is going snow skiing over
Christmas break and you are trying to decide
which company to rent the snow skis from.
How much will it cost to rent skis for 6 hours
from each company?
Skis for You ______________________
House
Ski Right ________________________
18.How much money would your family
save, per person, if you rent from Skis for
You?
In #14-16, determine if the following
numbers form a right triangle.
__________________________
14. 5cm, 13cm, 12cm
15. 78in, 72in, 30 in
16. 15ft, 10ft, 20ft
19.After hour many hours do the companies
charge the same amount?
__________________________________
20. Luke needs $104 to buy the bike he
wants. He saves $8 a week. Write and solve
an equation to find the number of weeks it
will take to have the money to buy the bike.
Equation ________________________
Solution (# of weeks) ______________
21. Chelsea’s Chains charges $6 to rent a
helmet plus $7 per hour. Cynthia’s Cycles
charges $3 to rent a helmet plus $8 per
hour. For what number of miles do both
companies charge the same amount?
Use the distributive property to solve each
equation below.
23. –8(n – 5) = –2(-4n + 12)
24.
7(3k + 8) = 4(5k – 1)
22. Which situation can be represented by
the equation
100 – 2x = 140 – 6x?
A Tank A has 100 gallons of water and
gains 2 gallons per hour. Tank B has
140 gallons and gains 6 gallons per
hour. When will the tanks have the
same amount of water?
25. Howard is 14 years old. This is 8 years
younger than his sister Sabrina. Write and
solve an equation to find Sabrina’s age.
B Tank A has 100 gallons of water and
loses 2 gallons per hour. Tank B has
140 gallons and loses 6 gallons per
hour. When will the tanks have the
same amount of water?
C Tank A has 100 gallons of water and
gains 2 gallons per hour. Tank B has
140 gallons and gains 6 gallons per
hour. When will Tank A have more
water than Tank B?
D Tank A has 100 gallons of water and
loses 2 gallons per hour. Tank B has
140 gallons and loses 6 gallons per
hour. When will Tank A have more
water than Tank B?
Represent each statement as an equation.
27. Negative 5 times the difference
of a number and 3 is 9.
28. 6 pies more than three times
the amount Faith baked
yesterday is 27.
29. The product of 8 and a number, c, is 12
less than twice the number, c. Find the
number.
26. The table below shows the number of
books that 4 students bought at the book
store, along with other purchases they
made. Sawyer and Collin spent the same
amount. If each book costs the same
amount, write an equation to determine the
cost of each book.
Student
# of books
Other
purchases
Sawyer
5
$35
Michelle
6
$42
Collin
Erica
4
3
$40
$24
30. Devin has saved $725 for a new drum
set and lessons. His drum set costs
$475, and drum lessons are $25 per
hour. Determine how many hours of
lessons he can afford. (Set up and solve
the equation)
31. Your bill for the music plan on your
phone cost you $109.74 last year.
The plan charged you $10.99 for a yearly
fee and then $0.79 per song. Write and
solve an equation to determine the
number of songs you downloaded for the
year.
32. Gaby’s Gym charges a yearly fee of $75
plus $12.50 per session for a personal
trainer. A new fitness center charges a
yearly fee of $100 plus $10 per session
with a trainer. For how many sessions is
the cost of the two plans the same?
(Write and solve the equation)