Students can use this worksheet to practice translating real-world scenarios into algebraic equations and solving for the unknown variable.

Let's solve each of these one-variable word problems step by step, writing the equation and solving it.

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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?

Step 1: Let $ x $ = number of t-shirts Lily has
Bree has 33 t-shirts.

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

Step 2: Solve:
$$
x = 132 - 3 = 129
$$

✔ 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?

Step 1: Let $ x $ = the number

Equation:
$$
4x = 2x + 8
$$

Step 2: Solve:
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?

Step 1: Let $ x $ = cousin’s age

Pedro’s age: $ 2x + 8 $

Given: $ 2x + 8 = 30 $

Step 2: Solve:
$$
2x = 22 \Rightarrow x = 11
$$

✔ 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?

Step 1: Let $ h $ = number of hours

Total cost: $ 125 + 30h = 305 $

Step 2: Solve:
$$
30h = 305 - 125 = 180
\Rightarrow h = \frac{180}{30} = 6
$$

✔ 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.

Step 1: Let $ x $ = the number

Equation:
$$
2x + 10 = 24
$$

Step 2: Solve:
$$
2x = 14 \Rightarrow x = 7
$$

✔ 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?

Step 1: Let $ x $ = minutes read last week

This week: $ 2x + 10 = 120 $

Step 2: Solve:
$$
2x = 110 \Rightarrow x = 55
$$

✔ 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?

Step 1: Let the first even number be $ x $. Then the next two are $ x+2 $ and $ x+4 $.

Sum:
$$
x + (x+2) + (x+4) = 18
\Rightarrow 3x + 6 = 18
$$

Step 2: Solve:
$$
3x = 12 \Rightarrow x = 4
$$

So the numbers are: $ 4, 6, 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?

Step 1: Let $ x $ = weekly allowance

You give $ \frac{1}{3}x $ to charity, spend $8, and have $2 left.

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

Step 2: Simplify:
$$
\frac{2}{3}x - 8 = 2
\Rightarrow \frac{2}{3}x = 10
\Rightarrow x = 10 \cdot \frac{3}{2} = 15
$$

✔ Answer: Weekly allowance is $15.

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✔ Final Answers Summary:

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

Let me know if you'd like these written out in a formatted worksheet style!