Math word problems worksheet for elementary students.
A math worksheet titled "Word Problems" with ten questions involving basic arithmetic and algebra, including consecutive numbers, money calculations, and division. The worksheet includes spaces for name, teacher, score, and date, and is from Math-Aids.Com.
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Show Answer Key & Explanations
Step-by-step solution for: Algebra 1 Worksheets | Word Problems Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Algebra 1 Worksheets | Word Problems Worksheets
I'll solve each word problem step by step, showing my work and verifying the answers.
Problem 1: The sum of three consecutive numbers is eighty-four. What is the smallest of the three numbers?
Let me call the smallest number "n". Then the three consecutive numbers are: n, n+1, and n+2.
Their sum is: n + (n+1) + (n+2) = 84
Simplifying: 3n + 3 = 84
Subtracting 3 from both sides: 3n = 81
Dividing by 3: n = 27
Verification: 27 + 28 + 29 = 84 ✓
Problem 2: Tom sold half of his comic books and then bought six more. He now has twelve. How many did he begin with?
Working backwards:
- He ended with 12 comic books
- Before buying 6 more, he had: 12 - 6 = 6 comic books
- These 6 were half of what he originally had
- So he started with: 6 × 2 = 12 comic books
Wait, let me verify this forward: Start with 12, sell half (6), have 6 left, buy 6 more, end with 12. That works!
But let me double-check by setting up an equation:
Let x = original number
x/2 + 6 = 12
x/2 = 6
x = 12
Problem 3: Oceanside Bike Rental Shop charges 14 dollars plus 9 dollars an hour for renting a bike. Joan paid 86 dollars to rent a bike. How many hours did she pay to have the bike checked out?
Total cost = base fee + (hourly rate × hours)
86 = 14 + 9h
86 - 14 = 9h
72 = 9h
h = 8 hours
Verification: 14 + (9 × 8) = 14 + 72 = 86 ✓
Problem 4: The sum of three consecutive even numbers is 156. What is the smallest of the three numbers?
Let the smallest even number be "n". Then the three consecutive even numbers are: n, n+2, and n+4.
Their sum is: n + (n+2) + (n+4) = 156
Simplifying: 3n + 6 = 156
Subtracting 6 from both sides: 3n = 150
Dividing by 3: n = 50
Verification: 50 + 52 + 54 = 156 ✓
Problem 5: The sum of three consecutive odd numbers is one hundred and eleven. What is the smallest of the three numbers?
Let the smallest odd number be "n". Then the three consecutive odd numbers are: n, n+2, and n+4.
Their sum is: n + (n+2) + (n+4) = 111
Simplifying: 3n + 6 = 111
Subtracting 6 from both sides: 3n = 105
Dividing by 3: n = 35
Verification: 35 + 37 + 39 = 111 ✓
Problem 6: On Monday, 301 students went on a trip to the zoo. All 7 buses were filled and 7 students had to travel in cars. How many students were in each bus?
Total students = students in buses + students in cars
301 = (students per bus × 7) + 7
301 - 7 = 7 × (students per bus)
294 = 7 × (students per bus)
Students per bus = 294 ÷ 7 = 42
Verification: (42 × 7) + 7 = 294 + 7 = 301 ✓
Problem 7: Mike bought four new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only twenty-nine cards left. How many cards did Mike start with?
Working backwards:
- After the dog ate half, there were 29 cards left
- This means before the dog ate them, there were 29 × 2 = 58 cards
- Before Mike bought 4 new cards, he had 58 - 4 = 54 cards
Let me verify forward: Start with 54, add 4 = 58, dog eats half = 29 left. ✓
Using algebra: Let x = starting number
(x + 4)/2 = 29
x + 4 = 58
x = 54
Problem 8: Sara had 207 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost?
Amount spent on books = 207 - 18 = 189 dollars
Cost per book = 189 ÷ 9 = 21 dollars
Verification: 9 × 21 = 189, and 207 - 189 = 18 ✓
Problem 9: Benny spent half of his allowance going to the movies. He washed the family car and earned 8 dollars. What is his weekly allowance if he ended with 16 dollars?
Let x = weekly allowance
After spending half: x/2
After earning 8: x/2 + 8 = 16
x/2 = 16 - 8 = 8
x = 16
Verification: Allowance is 16, spend half (8), have 8 left, earn 8 more, end with 16. ✓
Problem 10: Sandy bought a soft drink for two dollars and five candy bars. She spent a total of seventeen dollars. How much did each candy bar cost?
Total spent = cost of soft drink + cost of candy bars
17 = 2 + (5 × cost per candy bar)
17 - 2 = 5 × cost per candy bar
15 = 5 × cost per candy bar
Cost per candy bar = 15 ÷ 5 = 3 dollars
Verification: 2 + (5 × 3) = 2 + 15 = 17 ✓
Final Answer:
1) 27
2) 12
3) 8 hours
4) 50
5) 35
6) 42 students
7) 54 cards
8) $21
9) $16
10) $3
Problem 1: The sum of three consecutive numbers is eighty-four. What is the smallest of the three numbers?
Let me call the smallest number "n". Then the three consecutive numbers are: n, n+1, and n+2.
Their sum is: n + (n+1) + (n+2) = 84
Simplifying: 3n + 3 = 84
Subtracting 3 from both sides: 3n = 81
Dividing by 3: n = 27
Verification: 27 + 28 + 29 = 84 ✓
Problem 2: Tom sold half of his comic books and then bought six more. He now has twelve. How many did he begin with?
Working backwards:
- He ended with 12 comic books
- Before buying 6 more, he had: 12 - 6 = 6 comic books
- These 6 were half of what he originally had
- So he started with: 6 × 2 = 12 comic books
Wait, let me verify this forward: Start with 12, sell half (6), have 6 left, buy 6 more, end with 12. That works!
But let me double-check by setting up an equation:
Let x = original number
x/2 + 6 = 12
x/2 = 6
x = 12
Problem 3: Oceanside Bike Rental Shop charges 14 dollars plus 9 dollars an hour for renting a bike. Joan paid 86 dollars to rent a bike. How many hours did she pay to have the bike checked out?
Total cost = base fee + (hourly rate × hours)
86 = 14 + 9h
86 - 14 = 9h
72 = 9h
h = 8 hours
Verification: 14 + (9 × 8) = 14 + 72 = 86 ✓
Problem 4: The sum of three consecutive even numbers is 156. What is the smallest of the three numbers?
Let the smallest even number be "n". Then the three consecutive even numbers are: n, n+2, and n+4.
Their sum is: n + (n+2) + (n+4) = 156
Simplifying: 3n + 6 = 156
Subtracting 6 from both sides: 3n = 150
Dividing by 3: n = 50
Verification: 50 + 52 + 54 = 156 ✓
Problem 5: The sum of three consecutive odd numbers is one hundred and eleven. What is the smallest of the three numbers?
Let the smallest odd number be "n". Then the three consecutive odd numbers are: n, n+2, and n+4.
Their sum is: n + (n+2) + (n+4) = 111
Simplifying: 3n + 6 = 111
Subtracting 6 from both sides: 3n = 105
Dividing by 3: n = 35
Verification: 35 + 37 + 39 = 111 ✓
Problem 6: On Monday, 301 students went on a trip to the zoo. All 7 buses were filled and 7 students had to travel in cars. How many students were in each bus?
Total students = students in buses + students in cars
301 = (students per bus × 7) + 7
301 - 7 = 7 × (students per bus)
294 = 7 × (students per bus)
Students per bus = 294 ÷ 7 = 42
Verification: (42 × 7) + 7 = 294 + 7 = 301 ✓
Problem 7: Mike bought four new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only twenty-nine cards left. How many cards did Mike start with?
Working backwards:
- After the dog ate half, there were 29 cards left
- This means before the dog ate them, there were 29 × 2 = 58 cards
- Before Mike bought 4 new cards, he had 58 - 4 = 54 cards
Let me verify forward: Start with 54, add 4 = 58, dog eats half = 29 left. ✓
Using algebra: Let x = starting number
(x + 4)/2 = 29
x + 4 = 58
x = 54
Problem 8: Sara had 207 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost?
Amount spent on books = 207 - 18 = 189 dollars
Cost per book = 189 ÷ 9 = 21 dollars
Verification: 9 × 21 = 189, and 207 - 189 = 18 ✓
Problem 9: Benny spent half of his allowance going to the movies. He washed the family car and earned 8 dollars. What is his weekly allowance if he ended with 16 dollars?
Let x = weekly allowance
After spending half: x/2
After earning 8: x/2 + 8 = 16
x/2 = 16 - 8 = 8
x = 16
Verification: Allowance is 16, spend half (8), have 8 left, earn 8 more, end with 16. ✓
Problem 10: Sandy bought a soft drink for two dollars and five candy bars. She spent a total of seventeen dollars. How much did each candy bar cost?
Total spent = cost of soft drink + cost of candy bars
17 = 2 + (5 × cost per candy bar)
17 - 2 = 5 × cost per candy bar
15 = 5 × cost per candy bar
Cost per candy bar = 15 ÷ 5 = 3 dollars
Verification: 2 + (5 × 3) = 2 + 15 = 17 ✓
Final Answer:
1) 27
2) 12
3) 8 hours
4) 50
5) 35
6) 42 students
7) 54 cards
8) $21
9) $16
10) $3
Parent Tip: Review the logic above to help your child master the concept of algebraic word problems worksheet.
