One Variable Word Problems Notes and Worksheets - Lindsay Bowden - Free Printable
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Step-by-step solution for: One Variable Word Problems Notes and Worksheets - Lindsay Bowden
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Step-by-step solution for: One Variable Word Problems Notes and Worksheets - Lindsay Bowden
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?
Let L = number of t-shirts Lily has.
Bree has 33 → 4 times that is 4 × 33 = 132
Lily has 3 less → L = 132 – 3
✔ Equation: L = 4(33) – 3
✔ Solution: L = 132 – 3 = 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?
Let x = the number.
4x = 2x + 8
✔ Equation: 4x = 2x + 8
Subtract 2x from both sides:
2x = 8
Divide by 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?
Let c = cousin’s age.
Pedro = 2c + 8
We know Pedro is 30 → 2c + 8 = 30
✔ Equation: 2c + 8 = 30
Subtract 8:
2c = 22
Divide by 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?
Let h = number of hours.
Total cost = 125 + 30h
Set equal to 305:
✔ Equation: 125 + 30h = 305
Subtract 125:
30h = 180
Divide by 30:
h = 6
Answer: Craig rented the car for 6 hours.
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Problem 5:
> 2 times a number increased by 10 is 24. Find the number.
Let x = the number.
“2 times a number increased by 10” → 2x + 10
Set equal to 24:
✔ Equation: 2x + 10 = 24
Subtract 10:
2x = 14
Divide by 2:
x = 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?
Let m = minutes read last week.
This week = 2m + 10
This week = 120 → 2m + 10 = 120
✔ Equation: 2m + 10 = 120
Subtract 10:
2m = 110
Divide by 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?
Let the middle even number be x. Then the three consecutive even numbers are:
x – 2, x, x + 2
Sum = (x – 2) + x + (x + 2) = 3x
Set equal to 18:
✔ Equation: 3x = 18
x = 6
So the numbers are:
6 – 2 = 4, 6, 6 + 2 = 8
Answer: The three numbers are 4, 6, and 8.
*(Check: 4 + 6 + 8 = 18 ✔️)*
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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?
Let a = weekly allowance.
You give away (1/3)a → remaining: a – (1/3)a = (2/3)a
Then you spend $8 → remaining: (2/3)a – 8
That equals $2:
✔ Equation: (2/3)a – 8 = 2
Add 8 to both sides:
(2/3)a = 10
Multiply both sides by 3:
2a = 30
Divide by 2:
a = 15
Answer: Your weekly allowance is $15.
*(Check: 1/3 of 15 = $5 given to charity → $10 left. Spend $8 → $2 left ✔️)*
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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 written out in a printable format or with diagrams!
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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?
Let L = number of t-shirts Lily has.
Bree has 33 → 4 times that is 4 × 33 = 132
Lily has 3 less → L = 132 – 3
✔ Equation: L = 4(33) – 3
✔ Solution: L = 132 – 3 = 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?
Let x = the number.
4x = 2x + 8
✔ Equation: 4x = 2x + 8
Subtract 2x from both sides:
2x = 8
Divide by 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?
Let c = cousin’s age.
Pedro = 2c + 8
We know Pedro is 30 → 2c + 8 = 30
✔ Equation: 2c + 8 = 30
Subtract 8:
2c = 22
Divide by 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?
Let h = number of hours.
Total cost = 125 + 30h
Set equal to 305:
✔ Equation: 125 + 30h = 305
Subtract 125:
30h = 180
Divide by 30:
h = 6
Answer: Craig rented the car for 6 hours.
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Problem 5:
> 2 times a number increased by 10 is 24. Find the number.
Let x = the number.
“2 times a number increased by 10” → 2x + 10
Set equal to 24:
✔ Equation: 2x + 10 = 24
Subtract 10:
2x = 14
Divide by 2:
x = 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?
Let m = minutes read last week.
This week = 2m + 10
This week = 120 → 2m + 10 = 120
✔ Equation: 2m + 10 = 120
Subtract 10:
2m = 110
Divide by 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?
Let the middle even number be x. Then the three consecutive even numbers are:
x – 2, x, x + 2
Sum = (x – 2) + x + (x + 2) = 3x
Set equal to 18:
✔ Equation: 3x = 18
x = 6
So the numbers are:
6 – 2 = 4, 6, 6 + 2 = 8
Answer: The three numbers are 4, 6, and 8.
*(Check: 4 + 6 + 8 = 18 ✔️)*
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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?
Let a = weekly allowance.
You give away (1/3)a → remaining: a – (1/3)a = (2/3)a
Then you spend $8 → remaining: (2/3)a – 8
That equals $2:
✔ Equation: (2/3)a – 8 = 2
Add 8 to both sides:
(2/3)a = 10
Multiply both sides by 3:
2a = 30
Divide by 2:
a = 15
Answer: Your weekly allowance is $15.
*(Check: 1/3 of 15 = $5 given to charity → $10 left. Spend $8 → $2 left ✔️)*
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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 written out in a printable format or with diagrams!
Parent Tip: Review the logic above to help your child master the concept of linear equation word problems worksheet.
