Here is the complete solution to all 8 word problems from the worksheet “ONE VARIABLE WORD PROBLEMS practice 2”. Each problem is solved by writing an equation and then solving it step-by-step.
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Problem 1:
> Lily has 3 less than 4 times the amount of t-shirts as Bree. If Bree has 33 t-shirts, how many does Lily have?
Equation:
Let L = number of t-shirts Lily has.
L = 4 × (Bree’s t-shirts) – 3
L = 4 × 33 – 3
Solution:
L = 132 – 3
L =
129
✔ Answer: Lily has 129 t-shirts.
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Problem 2:
> 4 times a number is equivalent to 8 more than 2 times the number. What is the number?
Equation:
Let x = the number.
4x = 2x + 8
Solution:
Subtract 2x from both sides:
4x – 2x = 8
2x = 8
x = 8 ÷ 2
x =
4
✔ Answer: The number is 4.
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Problem 3:
> Pedro is 8 years older than twice the age of his cousin. If Pedro is 30, how old is his cousin?
Equation:
Let c = cousin’s age.
Pedro’s age = 2c + 8
30 = 2c + 8
Solution:
Subtract 8 from both sides:
30 – 8 = 2c
22 = 2c
c = 22 ÷ 2
c =
11
✔ Answer: His cousin is 11 years old.
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Problem 4:
> A car rental service charges a rental fee of $125 plus $30 per hour to rent a car. If Craig’s total bill is $305, how many hours did he have the rental car?
Equation:
Let h = number of hours.
Total cost = 125 + 30h
305 = 125 + 30h
Solution:
Subtract 125 from both sides:
305 – 125 = 30h
180 = 30h
h = 180 ÷ 30
h =
6
✔ Answer: Craig had the car for 6 hours.
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Problem 5:
> 2 times a number increased by 10 is 24. Find the number.
Equation:
Let n = the number.
2n + 10 = 24
Solution:
Subtract 10 from both sides:
2n = 24 – 10
2n = 14
n = 14 ÷ 2
n =
7
✔ Answer: The number is 7.
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Problem 6:
> Kyla spent 120 minutes reading this week. If this was 10 more than 2 times the amount of time she spent reading last week, how many minutes did she read last week?
Equation:
Let m = minutes read last week.
This week = 2m + 10
120 = 2m + 10
Solution:
Subtract 10 from both sides:
120 – 10 = 2m
110 = 2m
m = 110 ÷ 2
m =
55
✔ Answer: She read 55 minutes last week.
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Problem 7:
> The sum of 3 consecutive even numbers is 18. What are the three numbers?
Equation:
Let the first even number = x
Then next two consecutive even numbers = x+2, x+4
Sum: x + (x+2) + (x+4) = 18
Solution:
Combine like terms:
3x + 6 = 18
Subtract 6 from both sides:
3x = 12
x = 4
So the numbers are:
x = 4
x+2 = 6
x+4 = 8
✔ Answer: The three numbers are 4, 6, and 8.
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Problem 8:
> You give a third of your weekly allowance to a charity. Then you spend $8 at the mall. If you have $2 left to spend, how much is your weekly allowance?
Equation:
Let A = weekly allowance.
After giving away ⅓A, you have ⅔A left.
Then you spend $8, so:
⅔A – 8 = 2
Solution:
Add 8 to both sides:
⅔A = 10
Multiply both sides by 3/2:
A = 10 × (3/2)
A = 30/2
A =
15
✔ Answer: Your weekly allowance is $15.
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✔ Final Answers Summary:
1.
129 t-shirts
2.
4
3.
11 years old
4.
6 hours
5.
7
6.
55 minutes
7.
4, 6, 8
8.
$15
Let me know if you’d like to see these problems graphed or explained differently!
Parent Tip: Review the logic above to help your child master the concept of solving equations word problems worksheet.
