Let’s work through each problem one by one using proportional reasoning. That means we’ll find the rate (like “per minute” or “per hour”) and then use that to find the answer for the new amount.
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Problem 1:
Sam reads 3 bags in 6 minutes. How long to read 5 bags?
Step 1: Find how long it takes to read 1 bag.
→ 6 minutes ÷ 3 bags = 2 minutes per bag.
Step 2: Multiply by 5 bags.
→ 2 minutes/bag × 5 bags = 10 minutes.
✔ Final Answer for #1:
10 minutes
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Problem 2:
Amy earns $25 in 3 hours. How much for 7 hours?
Step 1: Find her hourly rate.
→ $25 ÷ 3 hours ≈ $8.333... per hour.
Step 2: Multiply by 7 hours.
→ $8.333... × 7 = $58.333...
Round to nearest tenth →
$58.3
✔ Final Answer for #2:
$58.3
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Problem 3:
Gym membership: $65 for 2 months. How much for 8 months?
Step 1: Find cost per month.
→ $65 ÷ 2 = $32.50 per month.
Step 2: Multiply by 8 months.
→ $32.50 × 8 = $260.00
✔ Final Answer for #3:
$260.0
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Problem 4:
Bobby drives 10 miles on 5 gallons. How far on 8 gallons?
Step 1: Find miles per gallon.
→ 10 miles ÷ 5 gallons = 2 miles per gallon.
Step 2: Multiply by 8 gallons.
→ 2 mpg × 8 gal = 16 miles.
✔ Final Answer for #4:
16 miles
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Problem 5:
Mary ran 2 miles in 23 minutes. How long to run 10 miles?
Step 1: Find time per mile.
→ 23 minutes ÷ 2 miles = 11.5 minutes per mile.
Step 2: Multiply by 10 miles.
→ 11.5 min/mile × 10 miles = 115 minutes.
✔ Final Answer for #5:
115 minutes
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Final Answer:
1. 10 minutes
2. $58.3
3. $260.0
4. 16 miles
5. 115 minutes
Parent Tip: Review the logic above to help your child master the concept of proportion word problem worksheet.
