Mixed Practice Set
Learn
This final lesson combines all your multi-step problem-solving skills. You'll break down problems, use diagrams when helpful, check your work, and avoid common mistakes. This is just like a real test!
Final Reminders
- Read the whole problem twice before starting.
- Identify what you need to find.
- Plan your steps before calculating.
- Show your work clearly.
- Check that your answer makes sense.
- Watch out for common mistakes!
Practice Quiz
This mixed practice set includes a variety of multi-step problems. Take your time and show your work for each one.
1. A movie theater has 12 rows with 18 seats in each row. For the afternoon show, 157 seats are filled. How many seats are empty?
Show Answer
59 empty seats
Step 1: Total seats = 12 x 18 = 216 seats
Step 2: Empty seats = 216 - 157 = 59 seats
2. Sophie saved $35 from her allowance. Her grandmother gave her $20 for her birthday. She wants to buy a game that costs $48. How much money will she have left after buying the game?
Show Answer
$7
Step 1: Total money = $35 + $20 = $55
Step 2: After buying game = $55 - $48 = $7
3. A school ordered 8 packages of paper. Each package has 500 sheets. The school uses 275 sheets each day. How many sheets will be left after 10 days?
Show Answer
1,250 sheets
Step 1: Total sheets = 8 x 500 = 4,000 sheets
Step 2: Sheets used in 10 days = 275 x 10 = 2,750 sheets
Step 3: Sheets left = 4,000 - 2,750 = 1,250 sheets
4. Kevin has 3 times as many trading cards as his sister. His sister has 28 cards. If Kevin gives away 15 cards, how many will he have?
Show Answer
69 cards
Step 1: Kevin's cards = 3 x 28 = 84 cards
Step 2: After giving away = 84 - 15 = 69 cards
5. A pizza shop made 15 pizzas. Each pizza was cut into 8 slices. They sold 94 slices. How many slices are left?
Show Answer
26 slices
Step 1: Total slices = 15 x 8 = 120 slices
Step 2: Slices left = 120 - 94 = 26 slices
6. Mrs. Lee has 96 stickers to share equally among 8 students. After sharing, each student uses 5 stickers for a project. How many stickers does each student have left?
Show Answer
7 stickers each
Step 1: Each student gets = 96 / 8 = 12 stickers
Step 2: After using 5 = 12 - 5 = 7 stickers
7. A store has 4 shelves of books. Each shelf has 32 books. The store sells 47 books and then receives a shipment of 25 new books. How many books are in the store now?
Show Answer
106 books
Step 1: Starting books = 4 x 32 = 128 books
Step 2: After selling = 128 - 47 = 81 books
Step 3: After shipment = 81 + 25 = 106 books
8. A rectangular garden is 14 feet long and 9 feet wide. A path that is 3 feet wide runs along one of the long sides. What is the perimeter of just the garden (not including the path)?
Show Answer
46 feet
The path information is extra - we only need the garden's perimeter.
Perimeter = 2 x (14 + 9) = 2 x 23 = 46 feet
(Or: 14 + 9 + 14 + 9 = 46 feet)
9. For a field trip, 156 students need to ride in vans. Each van holds 12 students. How many vans are needed so that all students have a seat?
Show Answer
13 vans
156 / 12 = 13 exactly
So 13 vans are needed with no empty seats.
10. Challenge Problem: A store sells juice boxes in packs of 6 for $4 each pack, or individually for $1 each. If you need exactly 20 juice boxes, what is the cheapest way to buy them and how much will it cost?
Show Answer
$14 (buy 3 packs + 2 individual)
Option 1: Buy 4 packs (24 boxes) = 4 x $4 = $16 (but 4 extra boxes)
Option 2: Buy 3 packs (18 boxes) + 2 individual = $12 + $2 = $14
Option 3: Buy 20 individual = 20 x $1 = $20
The cheapest is Option 2: 3 packs + 2 individual = $14
Check Your Understanding
How did you do? Count your correct answers:
- 9-10 correct: Excellent! You've mastered multi-step word problems!
- 7-8 correct: Great job! Review the problems you missed.
- 5-6 correct: Good effort! Consider reviewing earlier lessons.
- Below 5: Go back and review each lesson in this unit.
Next Steps
- Congratulations on completing the Multi-Step Word Problems unit!
- Keep practicing these skills in your daily math work
- Remember: Break problems into steps, show your work, and check your answers!
- You're building important skills for the SAT and ACT!