Two-Step Equation Word Problems

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Date:

📝 Part 1: Set Up and Solve

Instructions: Read each problem carefully. Write the equation, then solve for the variable. Show your work!

1. Sarah bought a notebook for $3 and some pens that cost $2 each. She spent $15 total. How many pens did she buy?

Equation: ________________

Answer: _______ pens

2. A gym charges a $25 membership fee plus $8 per month. If Jake paid $73 total, how many months was his membership?

Equation: ________________

Answer: _______ months

3. Maria had some money. She spent $12 on lunch and then spent half of what remained on a book that cost $9. How much money did she start with?

Equation: ________________

Answer: $_______

4. A plumber charges $50 for a house call plus $35 per hour. If the total bill was $155, how many hours did the plumber work?

Equation: ________________

Answer: _______ hours

🎯 Part 2: Multiple Choice

Instructions: Choose the correct equation for each word problem.

5. Tom's age plus 7 years equals 3 times his current age minus 1. Which equation represents this?

x + 7 = 3x - 1

x + 7 = 3(x - 1)

7x = 3x - 1

x + 7 = 3 + x - 1

6. A taxi ride costs $4 plus $0.75 per mile. If the total cost was $13, which equation finds the number of miles?

4x + 0.75 = 13

4 + 0.75x = 13

4 + 0.75 + x = 13

(4 + 0.75)x = 13

7. Lisa bought 4 identical shirts and paid a $6 shipping fee. Her total was $54. What was the cost of each shirt?

$10

$12

$15

$18

8. The temperature dropped 5°F each hour for several hours. If it started at 68°F and ended at 48°F, for how many hours did it drop?

3 hours

4 hours

5 hours

6 hours

🔧 Part 3: Problem Solving

9. Create your own two-step equation word problem about buying items at a store. Include a fixed cost and a per-item cost.

10. Explain in your own words what makes an equation a "two-step" equation.

Answer Key - Two-Step Equation Word Problems

📝 Part 1: Set Up and Solve - ANSWERS

1. Sarah bought a notebook for $3 and some pens that cost $2 each. She spent $15 total. How many pens did she buy?

Equation: 3 + 2x = 15

Solution: 2x = 12, so x = 6

Answer: 6 pens

2. A gym charges a $25 membership fee plus $8 per month. If Jake paid $73 total, how many months was his membership?

Equation: 25 + 8x = 73

Solution: 8x = 48, so x = 6

Answer: 6 months

3. Maria had some money. She spent $12 on lunch and then spent half of what remained on a book that cost $9. How much money did she start with?

Equation: (x - 12) ÷ 2 = 9 or (x - 12)/2 = 9

Solution: x - 12 = 18, so x = 30

Answer: $30

4. A plumber charges $50 for a house call plus $35 per hour. If the total bill was $155, how many hours did the plumber work?

Equation: 50 + 35x = 155

Solution: 35x = 105, so x = 3

Answer: 3 hours

🎯 Part 2: Multiple Choice - ANSWERS

5. Tom's age plus 7 years equals 3 times his current age minus 1.

Answer: x + 7 = 3x - 1

6. A taxi ride costs $4 plus $0.75 per mile. If the total cost was $13, which equation finds the number of miles?

Answer: 4 + 0.75x = 13

7. Lisa bought 4 identical shirts and paid a $6 shipping fee. Her total was $54. What was the cost of each shirt?

Equation: 4x + 6 = 54

Answer: $12

8. The temperature dropped 5°F each hour for several hours. If it started at 68°F and ended at 48°F, for how many hours did it drop?

Equation: 68 - 5x = 48

Answer: 4 hours

🔧 Part 3: Problem Solving - SAMPLE ANSWERS

9. Create your own two-step equation word problem about buying items at a store.

Sample Answer: "Alex bought a backpack for $20 and some pencils that cost $3 each. He spent $35 total. How many pencils did he buy?" (Equation: 20 + 3x = 35)

10. Explain in your own words what makes an equation a "two-step" equation.

Sample Answer: A two-step equation requires exactly two operations to solve for the variable. Usually you need to add/subtract first, then multiply/divide (or vice versa) to isolate the variable.