Two-step equations - word problems - Free Printable

Let's solve each of the two-step equation word problems step by step.

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Problem 1:

Eduardo won 31 small prizes playing the bean bag toss at the county fair. At school, he gave 2 of his prizes to every student in his math class. Now he has 3 prizes left. Write and solve an equation to find x, the number of students in Eduardo's math class.

#### Step 1: Define the variable
Let $ x $ = number of students in Eduardo's math class.

#### Step 2: Set up the equation
Eduardo started with 31 prizes. He gave away 2 prizes per student, so he gave away $ 2x $ prizes. After giving them away, he had 3 left.

So:
$$
31 - 2x = 3
$$

#### Step 3: Solve the equation
$$
31 - 2x = 3
$$
Subtract 31 from both sides:
$$
-2x = 3 - 31
$$
$$
-2x = -28
$$
Divide both sides by -2:
$$
x = 14
$$

✔ Answer: There are 14 students in Eduardo's math class.

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Problem 2:

A family spent $52 on tickets to go to the circus. The circus tickets were $9.75 each and there was a $3.25 service fee for the order. Write and solve an equation to find x, the number of circus tickets the family bought.

#### Step 1: Define the variable
Let $ x $ = number of tickets bought.

#### Step 2: Set up the equation
Each ticket costs $9.75, so total cost for tickets is $ 9.75x $. Add the $3.25 service fee. Total spent is $52.

$$
9.75x + 3.25 = 52
$$

#### Step 3: Solve the equation
$$
9.75x + 3.25 = 52
$$
Subtract 3.25 from both sides:
$$
9.75x = 52 - 3.25
$$
$$
9.75x = 48.75
$$
Divide both sides by 9.75:
$$
x = \frac{48.75}{9.75} = 5
$$

✔ Answer: The family bought 5 tickets.

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Problem 3:

Jarret bought some old bikes at an auction for $350. He fixed each of the bikes and sold them for $50 each. He made a $6200 profit. Write and solve an equation to find x, the number of bikes Jarret sold.

#### Step 1: Define the variable
Let $ x $ = number of bikes sold.

#### Step 2: Set up the equation
He sold each bike for $50, so total revenue = $ 50x $.
He spent $350 to buy all the bikes.
Profit = Revenue - Cost

Given that profit = $6200:

$$
50x - 350 = 6200
$$

#### Step 3: Solve the equation
$$
50x - 350 = 6200
$$
Add 350 to both sides:
$$
50x = 6200 + 350 = 6550
$$
Divide by 50:
$$
x = \frac{6550}{50} = 131
$$

✔ Answer: Jarret sold 131 bikes.

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Problem 4:

Stanley sells rugs at his flooring store. He sells 2/3 of his rugs and then buys 128 more. He now has 327 rugs. Write and solve an equation to find x, the number of rugs Stanley had to begin with.

#### Step 1: Define the variable
Let $ x $ = number of rugs Stanley had initially.

#### Step 2: Set up the equation
He sells $ \frac{2}{3}x $, so he has $ x - \frac{2}{3}x = \frac{1}{3}x $ left.
Then he buys 128 more, so total rugs now:
$$
\frac{1}{3}x + 128 = 327
$$

#### Step 3: Solve the equation
$$
\frac{1}{3}x + 128 = 327
$$
Subtract 128 from both sides:
$$
\frac{1}{3}x = 327 - 128 = 199
$$
Multiply both sides by 3:
$$
x = 199 \times 3 = 597
$$

✔ Answer: Stanley originally had 597 rugs.

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✔ Final Answers:

1. 14 students
2. 5 tickets
3. 131 bikes
4. 597 rugs

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