Math word problems worksheet for practice and learning.
A worksheet titled "Word Problems" with six math word problems involving percentages, doubling money, perimeter, least common multiples, time calculations, and algebraic equations.
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Show Answer Key & Explanations
Step-by-step solution for: Practice Your Math Skills With These 7th Grade Worksheets | Word ...
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Show Answer Key & Explanations
Step-by-step solution for: Practice Your Math Skills With These 7th Grade Worksheets | Word ...
I'll solve each of these word problems step by step.
Problem 1: Basketball shots
- Sam sinks 65% of his shots
- He takes 30 shots
- Need to find: how many he will sink
Calculation: 65% of 30 = 0.65 × 30 = 19.5
Since you can't sink half a shot, we need to round. In this context, we'd typically round down since you can only count complete successful shots, so 19 shots. However, mathematically it's 19.5, which rounds to 20 if using standard rounding rules.
Let me verify: 30 × 0.65 = 19.5
Problem 2: Doubling penny allowance
Starting with $0.01 (one penny), doubling each day.
Day 1: $0.01
Day 2: $0.02
Day 3: $0.04
...and so on.
The formula is: Amount = $0.01 × 2^(day-1)
For over $1000:
$0.01 × 2^(n-1) > 1000
2^(n-1) > 100,000
Let me calculate powers of 2:
2^16 = 65,536
2^17 = 131,072
So on day 18 (when n-1 = 17): $0.01 × 131,072 = $1,310.72 ✓
For over $10,000:
$0.01 × 2^(n-1) > 10,000
2^(n-1) > 1,000,000
2^19 = 524,288
2^20 = 1,048,576
So on day 21 (when n-1 = 20): $0.01 × 1,048,576 = $10,485.76 ✓
On the 15th day:
Amount = $0.01 × 2^(15-1) = $0.01 × 2^14 = $0.01 × 16,384 = $163.84
Problem 3: Fence around pool
- Posts are 2 yards apart
- 4 posts along the width
- 8 posts along the length
Important: When counting posts in a line, if there are n posts, there are (n-1) spaces between them.
Width: 4 posts means 3 spaces, so width = 3 × 2 = 6 yards
Length: 8 posts means 7 spaces, so length = 7 × 2 = 14 yards
Total posts needed for a rectangle:
We need posts at all corners and along all sides.
- Along width (top): 4 posts
- Along width (bottom): 4 posts
- Along length (left side): 8 posts
- Along length (right side): 8 posts
But corners are counted twice! So:
Total = 4 + 4 + 8 + 8 - 4 (corners) = 20 posts
Wait, let me reconsider. If we have 4 posts along width and 8 along length, the corners are shared. Let me think differently:
Perimeter posts = 2(width posts) + 2(length posts) - 4(corners counted twice)
= 2(4) + 2(8) - 4 = 8 + 16 - 4 = 20 posts
Dimensions: Width = 6 yards, Length = 14 yards
Problem 4: Marbles divisible by 3, 5, or 6
Need the least common multiple (LCM) of 3, 5, and 6.
Prime factorization:
- 3 = 3
- 5 = 5
- 6 = 2 × 3
LCM = 2 × 3 × 5 = 30
Check: 30 ÷ 3 = 10 ✓, 30 ÷ 5 = 6 ✓, 30 ÷ 6 = 5 ✓
Problem 5: People born per time period
150 people per minute
Per hour: 150 × 60 minutes = 9,000 people/hour
Per day: 9,000 × 24 hours = 216,000 people/day
Per year: 216,000 × 365 days = 78,840,000 people/year
(Or if considering leap years, could use 365.25, but 365 is standard)
Problem 6: Parking lot sections
- Total spots: 800
- Section 1: 270 spots
- Section 2: has 150 more than section 3
- Section 3: unknown
Let x = spots in section 3
Then section 2 = x + 150
Total: 270 + (x + 150) + x = 800
270 + x + 150 + x = 800
420 + 2x = 800
2x = 380
x = 190
So section 3 = 190 spots
Section 2 = 190 + 150 = 340 spots
Check: 270 + 340 + 190 = 800 ✓
Final Answer:
1. 19.5 shots (or approximately 20 shots)
2. Day 18 for over $1000; Day 21 for over $10,000; $163.84 on day 15
3. 20 posts; dimensions are 6 yards wide by 14 yards long
4. 30 marbles
5. 9,000 per hour; 216,000 per day; 78,840,000 per year
6. 340 spots in section 2
Problem 1: Basketball shots
- Sam sinks 65% of his shots
- He takes 30 shots
- Need to find: how many he will sink
Calculation: 65% of 30 = 0.65 × 30 = 19.5
Since you can't sink half a shot, we need to round. In this context, we'd typically round down since you can only count complete successful shots, so 19 shots. However, mathematically it's 19.5, which rounds to 20 if using standard rounding rules.
Let me verify: 30 × 0.65 = 19.5
Problem 2: Doubling penny allowance
Starting with $0.01 (one penny), doubling each day.
Day 1: $0.01
Day 2: $0.02
Day 3: $0.04
...and so on.
The formula is: Amount = $0.01 × 2^(day-1)
For over $1000:
$0.01 × 2^(n-1) > 1000
2^(n-1) > 100,000
Let me calculate powers of 2:
2^16 = 65,536
2^17 = 131,072
So on day 18 (when n-1 = 17): $0.01 × 131,072 = $1,310.72 ✓
For over $10,000:
$0.01 × 2^(n-1) > 10,000
2^(n-1) > 1,000,000
2^19 = 524,288
2^20 = 1,048,576
So on day 21 (when n-1 = 20): $0.01 × 1,048,576 = $10,485.76 ✓
On the 15th day:
Amount = $0.01 × 2^(15-1) = $0.01 × 2^14 = $0.01 × 16,384 = $163.84
Problem 3: Fence around pool
- Posts are 2 yards apart
- 4 posts along the width
- 8 posts along the length
Important: When counting posts in a line, if there are n posts, there are (n-1) spaces between them.
Width: 4 posts means 3 spaces, so width = 3 × 2 = 6 yards
Length: 8 posts means 7 spaces, so length = 7 × 2 = 14 yards
Total posts needed for a rectangle:
We need posts at all corners and along all sides.
- Along width (top): 4 posts
- Along width (bottom): 4 posts
- Along length (left side): 8 posts
- Along length (right side): 8 posts
But corners are counted twice! So:
Total = 4 + 4 + 8 + 8 - 4 (corners) = 20 posts
Wait, let me reconsider. If we have 4 posts along width and 8 along length, the corners are shared. Let me think differently:
Perimeter posts = 2(width posts) + 2(length posts) - 4(corners counted twice)
= 2(4) + 2(8) - 4 = 8 + 16 - 4 = 20 posts
Dimensions: Width = 6 yards, Length = 14 yards
Problem 4: Marbles divisible by 3, 5, or 6
Need the least common multiple (LCM) of 3, 5, and 6.
Prime factorization:
- 3 = 3
- 5 = 5
- 6 = 2 × 3
LCM = 2 × 3 × 5 = 30
Check: 30 ÷ 3 = 10 ✓, 30 ÷ 5 = 6 ✓, 30 ÷ 6 = 5 ✓
Problem 5: People born per time period
150 people per minute
Per hour: 150 × 60 minutes = 9,000 people/hour
Per day: 9,000 × 24 hours = 216,000 people/day
Per year: 216,000 × 365 days = 78,840,000 people/year
(Or if considering leap years, could use 365.25, but 365 is standard)
Problem 6: Parking lot sections
- Total spots: 800
- Section 1: 270 spots
- Section 2: has 150 more than section 3
- Section 3: unknown
Let x = spots in section 3
Then section 2 = x + 150
Total: 270 + (x + 150) + x = 800
270 + x + 150 + x = 800
420 + 2x = 800
2x = 380
x = 190
So section 3 = 190 spots
Section 2 = 190 + 150 = 340 spots
Check: 270 + 340 + 190 = 800 ✓
Final Answer:
1. 19.5 shots (or approximately 20 shots)
2. Day 18 for over $1000; Day 21 for over $10,000; $163.84 on day 15
3. 20 posts; dimensions are 6 yards wide by 14 yards long
4. 30 marbles
5. 9,000 per hour; 216,000 per day; 78,840,000 per year
6. 340 spots in section 2
Parent Tip: Review the logic above to help your child master the concept of math problems for 7th graders worksheet.
