4-6 Writing Equations
Translate each sentence into an equation.
1. The quotient of a number and 3, less 8, is 16.
SOLUTION: Let n = a number.
2. Tiffani spent $95 for clothes. This is $15 more than 4 times the amount her sister spent for school supplies.
SOLUTION: Let s = the amount Tiffani’s sister spent for school supplies. Then 4s + 15 is the amount Tiffani spent for clothes.
4s + 15 = 95
3. Morgan has 98 baseball cards in his collection, which is twelve less than the product of 5 and the number of cards
Tyler has.
SOLUTION: Let t = the number of cards that Tyler has. Then 5t – 12 is the number of cards Morgan has.
5t – 12 = 98
Solve each problem by writing and solving an equation.
4. SHOPPING Kendra pays $132 for shoes and clothes. The clothes cost $54 more than the shoes. How much do the
shoes cost?
SOLUTION: Let s = the amount that the shoes cost. Then, s + 54 = the amount the clothes cost. The amount of the shoes plus the
amount of the clothes was $132.
The shoes cost $39.
5. CAR WASH During the spring car wash, the Activities Club washed 14 fewer cars than during the summer car
wash. They washed a total of 96 cars during both car washes. How many cars did they wash during the spring car
wash?
SOLUTION: Let x = the amount of cars washed during the summer car wash. Then, x – 14 = the amount of cars washed during
the spring car wash. The total amount of cars washed was 96.
The amount of cars washed during the summer car wash was 55. So, the amount of cars washed in the spring was
x – 14, or 55 – 14 = 41 cars.
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6. FITNESSA gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how
many months do you have a gym membership?
4-6 The
Writing
Equations
shoes cost
$39.
5. CAR WASH During the spring car wash, the Activities Club washed 14 fewer cars than during the summer car
wash. They washed a total of 96 cars during both car washes. How many cars did they wash during the spring car
wash?
SOLUTION: Let x = the amount of cars washed during the summer car wash. Then, x – 14 = the amount of cars washed during
the spring car wash. The total amount of cars washed was 96.
The amount of cars washed during the summer car wash was 55. So, the amount of cars washed in the spring was
x – 14, or 55 – 14 = 41 cars.
6. FITNESSA gym charges a $50 activation fee and $17 per month for a membership. If you spend $356, for how
many months do you have a gym membership?
SOLUTION: Let m = the number of months you have a membership. The total cost is the activation fee, $50, plus $17 per month,
or 17m.
You have the gym membership for 18 months.
Translate each sentence into an equation.
7. Eighteen more than twice a number is 8.
SOLUTION: Let x = a number.
8. The product of a number and 9, less 20 is 7.
SOLUTION: Let n = a number.
9. There are 48 soccer teams in the Springtown Association. This is three less than three times the number of teams in
the Lyon Association.
SOLUTION: Let x = the number of teams in the Lyon Association. Then 3x – 3 is the number of teams in the Springtown
Association.
3x – 3 = 48
10. Eileen swam for 85 minutes. This is 21 more minutes than 4 times the number of minutes Ethan swam.
SOLUTION: eSolutions
Let Manual
n = the- Powered
numberbyofCognero
minutes
4n + 21 = 85
Ethan swam. Then 4n + 21 is the number of minutes Eileen swam.
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SOLUTION: 4-6
Let x = the number of teams in the Lyon Association. Then 3x – 3 is the number of teams in the Springtown
Association.
Writing Equations
3x – 3 = 48
10. Eileen swam for 85 minutes. This is 21 more minutes than 4 times the number of minutes Ethan swam.
SOLUTION: Let n = the number of minutes Ethan swam. Then 4n + 21 is the number of minutes Eileen swam.
4n + 21 = 85
Solve each problem by writing and solving an equation.
11. BASKETBALL In 2007, Candace Parker, from the University of Tennessee, made 37 more field goals than she
did in 2006. She had a total of 497 field goals for those years. How many field goals did she make in 2006?
SOLUTION: Let g = the number of field goals made in 2006. Then g + 37 is the number of field goals made in 2007.
Candace made 230 field goals in 2006.
12. CARS The Marsh family took a vacation that covered a total distance of 1356 miles. The return trip was 284 miles
shorter than the first part of the trip. How long was the return trip?
SOLUTION: Let m = the number of miles on the first part of the trip. Then m – 284 is the number of miles for the return trip.
There were 820 miles on the first part of the trip. The return trip was 820 – 284, or 536 miles.
13. VIDEO GAMES Three friends share the cost of renting a game system. Each person also rents one game for
$8.50. If each person pays $13.25, what is the cost of renting the system?
SOLUTION: Let x = the cost of renting the system. Then
is the cost for each friend to rent the system.
It cost $14.25 to rent the system.
14. VACATION Suppose you purchase 3 identical T-shirts and a hat. The hat cost $21 and you spend $60 in all. How
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much does each T-shirt cost?
SOLUTION: Page 3
4-6 Writing Equations
It cost $14.25 to rent the system.
14. VACATION Suppose you purchase 3 identical T-shirts and a hat. The hat cost $21 and you spend $60 in all. How
much does each T-shirt cost?
SOLUTION: Let t = the cost of each T-shirt.
Each T-shirt cost $13.
15. BOOK FINES You return a book that was 6 days overdue. Including a previous unpaid balance of $0.90, your new
balance is $2.40. How much is the daily fine for an overdue book?
SOLUTION: Let d = the daily fine for an overdue book.
The daily fine for an overdue book is $0.25.
16. CONSTRUCTION Tao is building a door. The height of the door is 1 foot more than twice its width. If the door is
7 feet high, what is its width?
SOLUTION: Let w = the width of the door.
The width of the door is 3 feet.
17. ENTERTAINMENT In his DVD collection, Domingo has eight more than twice as many animated movies as
action movies. If he has 24 animated movies, write and solve an equation to find how many action movies are in his
collection.
SOLUTION: Let n = number of action movies.
Domingo has 8 action moves in his collection.
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