One Variable Word Problems Notes and Worksheets - Lindsay Bowden - Free Printable

Let’s solve each problem one by one. We’ll write an equation for each, then solve 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.
→ “4 times Bree’s shirts” = 4 × 33 = 132
→ “3 less than that” = 132 - 3 = 129

Equation:
L = 4×33 - 3
L = 132 - 3
L = 129

✔ 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 unknown number.
→ “4 times a number” = 4x
→ “8 more than 2 times the number” = 2x + 8

Equation:
4x = 2x + 8

Subtract 2x from both sides:
2x = 8

Divide by 2:
x = 4

✔ 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.
→ “Twice the cousin’s age” = 2c
→ “8 years older than that” = 2c + 8
→ That equals Pedro’s age: 30

Equation:
2c + 8 = 30

Subtract 8 from both sides:
2c = 22

Divide by 2:
c = 11

✔ Cousin is 11 years old.

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Problem 4:
A car rental service charges $125 plus $30 per hour. Craig’s total bill is $305. How many hours did he rent the car?

→ Let h = number of hours.
→ Total cost = 125 + 30h
→ Set equal to 305

Equation:
125 + 30h = 305

Subtract 125 from both sides:
30h = 180

Divide by 30:
h = 6

✔ He 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 n = the number.
→ “2 times a number” = 2n
→ “Increased by 10” = 2n + 10
→ Equals 24

Equation:
2n + 10 = 24

Subtract 10:
2n = 14

Divide by 2:
n = 7

✔ The number is 7.

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Problem 6:
Kyla spent 120 minutes reading this week. This was 10 more than 2 times last week’s time. How many minutes did she read last week?

→ Let m = minutes read last week.
→ “2 times last week” = 2m
→ “10 more than that” = 2m + 10
→ Equals 120

Equation:
2m + 10 = 120

Subtract 10:
2m = 110

Divide by 2:
m = 55

✔ 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?

→ Consecutive even numbers go up by 2 (like 2, 4, 6 or 10, 12, 14).
→ Let the first even number be x.
→ Then next two are x+2 and x+4.

Sum:
x + (x+2) + (x+4) = 18

Combine like terms:
3x + 6 = 18

Subtract 6:
3x = 12

Divide by 3:
x = 4

So the numbers are:
4, 6, 8

Check: 4 + 6 + 8 = 18 ✔

✔ The three numbers are 4, 6, and 8.

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Problem 8:
You give a third of your weekly allowance to charity. Then you spend $8 at the mall. You have $2 left. How much is your weekly allowance?

→ Let A = weekly allowance.
→ Give away 1/3 → so you keep 2/3 of A.
→ Then spend $8 → now you have $2 left.

So:
(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

Check:
Allowance = $15
Give 1/3 to charity → $5 given, $10 left
Spend $8 → $2 left ✔

✔ Weekly allowance is $15.

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Final Answer:
1. 129
2. 4
3. 11
4. 6
5. 7
6. 55
7. 4, 6, 8
8. 15