Sure! Let’s solve each of the 6 ratio and proportion word problems step by step, showing all workings.
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Problem 1:
> 2 kilograms of apples cost $2.50. How many grams of apples can you buy for $20?
Step 1: Find cost per kilogram.
- $2.50 for 2 kg → cost per kg = $2.50 ÷ 2 =
$1.25 per kg
Step 2: Find how many kg you can buy for $20.
- $20 ÷ $1.25 per kg =
16 kg
Step 3: Convert kg to grams (1 kg = 1000 grams).
- 16 kg × 1000 =
16,000 grams
✔ Answer: 16,000 grams
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Problem 2:
> A truck can drive 200 kilometers on 25 liters of gasoline. How many liters of gasoline do I need to drive 640 kilometers?
This is a direct proportion.
Set up a proportion:
> 200 km → 25 liters
> 640 km → x liters
So,
> 200 / 25 = 640 / x
OR better:
> 200 : 25 = 640 : x
→ Cross multiply:
200x = 25 × 640
200x = 16,000
x = 16,000 ÷ 200 =
80
✔ Answer: 80 liters
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Problem 3:
> A car can travel 120 miles in 90 minutes. How many hours will it take you to drive 160 miles?
First, find speed in miles per minute or miles per hour.
Method: Use proportion
120 miles → 90 minutes
160 miles → x minutes
Set up:
> 120 / 90 = 160 / x
Cross multiply:
120x = 90 × 160
120x = 14,400
x = 14,400 ÷ 120 =
120 minutes
Convert to hours: 120 minutes ÷ 60 =
2 hours
✔ Answer: 2 hours
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Problem 4:
> I can type 100 words per 120 seconds. How many words can I type in 7 minutes?
First, convert 7 minutes to seconds:
> 7 × 60 =
420 seconds
Now set up proportion:
100 words → 120 seconds
x words → 420 seconds
> 100 / 120 = x / 420
Cross multiply:
120x = 100 × 420
120x = 42,000
x = 42,000 ÷ 120 =
350
✔ Answer: 350 words
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Problem 5:
> A chicken can lay 1 egg per 2 days. How many hours will it take the chicken to lay 5 eggs?
First, find total days for 5 eggs:
> 1 egg → 2 days
> 5 eggs → 5 × 2 =
10 days
Convert days to hours:
> 10 days × 24 hours/day =
240 hours
✔ Answer: 240 hours
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Problem 6:
> I can run 6 kilometers per hour at a steady pace. How long will it take me to run 10 kilometers?
Use formula: Time = Distance ÷ Speed
> Time = 10 km ÷ 6 km/h = 10/6 hours = 5/3 hours
Convert to mixed number or decimal:
> 5/3 = 1 2/3 hours
Or in minutes: 1 hour + (2/3 × 60) = 1 hour 40 minutes
✔ Answer: 1 2/3 hours (or 1 hour 40 minutes)
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✔ Final Answers Summary:
1.
16,000 grams
2.
80 liters
3.
2 hours
4.
350 words
5.
240 hours
6.
1 2/3 hours (or 1 hour 40 minutes)
Let me know if you’d like these explained with diagrams or tables too!
Parent Tip: Review the logic above to help your child master the concept of 7th grade proportion word problem worksheet.
