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

Let's solve each of these one-variable word problems step by step. For each problem, we will:

1. Define a variable.
2. Write an equation based on the scenario.
3. Solve the equation.
4. Provide the final answer.

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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 $ x $ = number of t-shirts Lily has.
- Bree has 33 t-shirts.
- "Lily has 3 less than 4 times Bree’s t-shirts":
$ x = 4(33) - 3 $

Equation:
$ x = 4(33) - 3 $
$ x = 132 - 3 $
$ x = 129 $

✔ Answer: Lily has 129 t-shirts.

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2. 4 times a number is equivalent to 8 more than 2 times the number. What is the number?

- Let $ x $ = the 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 $

✔ Answer: The number is 4.

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3. Pedro is 8 years older than twice the age of his cousin. If Pedro is 30, how old is his cousin?

- Let $ x $ = cousin’s age.
- “Twice the age of his cousin” → $ 2x $
- “8 years older than that” → $ 2x + 8 $
- Pedro is 30:
$ 2x + 8 = 30 $

Equation:
$ 2x + 8 = 30 $

Subtract 8:
$ 2x = 22 $

Divide by 2:
$ x = 11 $

✔ Answer: His cousin is 11 years old.

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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 = 305 $

Equation:
$ 125 + 30h = 305 $

Subtract 125:
$ 30h = 180 $

Divide by 30:
$ h = 6 $

✔ Answer: Craig had the car for 6 hours.

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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 $
- Equals 24:
$ 2x + 10 = 24 $

Equation:
$ 2x + 10 = 24 $

Subtract 10:
$ 2x = 14 $

Divide by 2:
$ x = 7 $

✔ Answer: The number is 7.

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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 $ x $ = minutes read last week.
- “10 more than 2 times last week” → $ 2x + 10 $
- This equals 120:
$ 2x + 10 = 120 $

Equation:
$ 2x + 10 = 120 $

Subtract 10:
$ 2x = 110 $

Divide by 2:
$ x = 55 $

✔ Answer: She read 55 minutes last week.

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7. The sum of 3 consecutive even numbers is 18. What are the three numbers?

- Let the first even number be $ x $.
- Then the next two consecutive even numbers are $ x+2 $ and $ x+4 $.
- Sum: $ x + (x+2) + (x+4) = 18 $

Equation:
$ x + x + 2 + x + 4 = 18 $
$ 3x + 6 = 18 $

Subtract 6:
$ 3x = 12 $

Divide by 3:
$ 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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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 $ x $ = weekly allowance.
- Give $ \frac{1}{3}x $ to charity.
- Spend $8 at mall.
- Left with $2.

So:
$ x - \frac{1}{3}x - 8 = 2 $

Equation:
$ \frac{2}{3}x - 8 = 2 $

Add 8 to both sides:
$ \frac{2}{3}x = 10 $

Multiply both sides by $ \frac{3}{2} $:
$ x = 10 \cdot \frac{3}{2} = 15 $

✔ Answer: Weekly allowance is $15.

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✔ Final Answers Summary:

| Problem | Equation | Answer |
|--------|---------|--------|
| 1 | $ x = 4(33) - 3 $ | 129 t-shirts |
| 2 | $ 4x = 2x + 8 $ | 4 |
| 3 | $ 2x + 8 = 30 $ | 11 years old |
| 4 | $ 125 + 30h = 305 $ | 6 hours |
| 5 | $ 2x + 10 = 24 $ | 7 |
| 6 | $ 2x + 10 = 120 $ | 55 minutes |
| 7 | $ 3x + 6 = 18 $ | 4, 6, 8 |
| 8 | $ \frac{2}{3}x - 8 = 2 $ | $15 |

Let me know if you'd like these written out neatly for printing or submission!