Two Step Word Problems with Addition and Subtraction - Free Printable

Let's solve each of the two-step equation word problems step by step. We'll write an equation for each problem and then solve it.

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Problem 1:

Carla is a waitress at Daybreak Diner, and she earns $5 for each hour she works. Last week, she earned $148 total, including $68 in tips. How many hours did Carla work last week?

#### Step 1: Define the variable
Let $ h $ = number of hours Carla worked.

She earns $5 per hour, so her earnings from work are $ 5h $.
She also earned $68 in tips.
Total earnings = $ 5h + 68 $

We know total earnings = $148

So:
$$
5h + 68 = 148
$$

#### Step 2: Solve the equation
Subtract 68 from both sides:
$$
5h = 148 - 68 = 80
$$

Divide by 5:
$$
h = \frac{80}{5} = 16
$$

✔ Answer: Carla worked 16 hours.

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Problem 2:

Mr. Olin bought 6 sketchbooks for the students in his art class. Each sketchbook was on sale for $3 off. If the sketchbooks cost $18 total before tax, what was the original price of each sketchbook?

#### Step 1: Define the variable
Let $ x $ = original price of one sketchbook.

Each sketchbook was discounted by $3, so sale price = $ x - 3 $

He bought 6 sketchbooks, so total cost:
$$
6(x - 3) = 18
$$

#### Step 2: Solve the equation
$$
6(x - 3) = 18
$$

Divide both sides by 6:
$$
x - 3 = 3
$$

Add 3 to both sides:
$$
x = 6
$$

✔ Answer: The original price of each sketchbook was $6.

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Problem 3:

Davion wants to buy 4 tickets to a basketball game. He sees that there is a discount for $25 off his entire purchase at checkout, so the tickets would cost him $215 before tax. What was the original price of each ticket?

#### Step 1: Define the variable
Let $ p $ = original price of one ticket.

He buys 4 tickets, so total original cost = $ 4p $

After $25 discount, he pays $215:
$$
4p - 25 = 215
$$

#### Step 2: Solve the equation
Add 25 to both sides:
$$
4p = 240
$$

Divide by 4:
$$
p = 60
$$

✔ Answer: The original price of each ticket was $60.

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Problem 4:

Elana makes knit hats and scarves and sells them in her online store for $12 each. Last week, Elana’s store made $180 total. If she sold 8 hats, how many scarves did she sell?

#### Step 1: Define the variable
Let $ s $ = number of scarves sold.

Each item (hat or scarf) sells for $12.

She sold 8 hats → $ 8 \times 12 = 96 $ from hats.

Total revenue = $ 180 $

So:
$$
12s + 96 = 180
$$

#### Step 2: Solve the equation
Subtract 96 from both sides:
$$
12s = 84
$$

Divide by 12:
$$
s = 7
$$

✔ Answer: Elana sold 7 scarves.

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Problem 5:

Tiana bought 3 video games that each cost the same amount. The tax on each video game was $1.29. She paid a total of $68.37 after tax. What was the price of each video game, before tax?

#### Step 1: Define the variable
Let $ g $ = price of one video game before tax.

Each game has tax of $1.29, so total cost per game = $ g + 1.29 $

She bought 3 games:
$$
3(g + 1.29) = 68.37
$$

#### Step 2: Solve the equation
First, divide both sides by 3:
$$
g + 1.29 = \frac{68.37}{3} = 22.79
$$

Subtract 1.29:
$$
g = 22.79 - 1.29 = 21.50
$$

✔ Answer: Each video game cost $21.50 before tax.

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Problem 6:

The local pool near Paxton’s house charges a one-time registration fee of $18.25 and $17.50 per month. Last year, Paxton paid $105.75. How many months was Paxton a member of the pool?

#### Step 1: Define the variable
Let $ m $ = number of months Paxton was a member.

Monthly cost = $17.50 → total monthly cost = $ 17.50m $

Plus one-time fee: $18.25

Total paid:
$$
17.50m + 18.25 = 105.75
$$

#### Step 2: Solve the equation
Subtract 18.25 from both sides:
$$
17.50m = 105.75 - 18.25 = 87.50
$$

Divide by 17.50:
$$
m = \frac{87.50}{17.50} = 5
$$

✔ Answer: Paxton was a member for 5 months.

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✔ Final Answers Summary:

1. 16 hours
2. $6
3. $60
4. 7 scarves
5. $21.50
6. 5 months

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