Ratio and Proportion Word Problems Worksheet 1

Let's solve each problem step by step with clear explanations.

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1. A Java book is comprised of two sections: core and advanced Java in the ratio 7:2. How much of each type of content will be needed to make a book of 450 pages?

Step 1: The ratio is 7:2, meaning for every 7 parts of core, there are 2 parts of advanced.

Total parts = 7 + 2 = 9

Each part = 450 ÷ 9 = 50 pages

- Core Java = 7 × 50 = 350 pages
- Advanced Java = 2 × 50 = 100 pages

✔ Answer: Core = 350 pages, Advanced = 100 pages

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2. 30 girls and boys have planned for a picnic. There is a ratio of 3 girls to 7 boys. How many boys are there?

Ratio of girls : boys = 3:7
Total parts = 3 + 7 = 10

Total people = 30

Each part = 30 ÷ 10 = 3

Number of boys = 7 × 3 = 21 boys

✔ Answer: 21 boys

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3. 12 miles is approximately equal to 6 km. How many km are equal to 18 miles? How many miles are equal to 42 km?

We know:
12 miles = 6 km → So, 1 mile = 6 ÷ 12 = 0.5 km
Or, 1 km = 12 ÷ 6 = 2 miles

Part A: 18 miles to km
18 × 0.5 = 9 km

Part B: 42 km to miles
42 × 2 = 84 miles

✔ Answer: 18 miles = 9 km; 42 km = 84 miles

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4. 5 pizzas cost $60. What will 9 pizzas cost?

Cost per pizza = 60 ÷ 5 = $12
Cost of 9 pizzas = 9 × 12 = $108

✔ Answer: $108

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5. 6 stuffed peppers cost $36. What will 12 stuffed peppers cost?

Cost per pepper = 36 ÷ 6 = $6
Cost of 12 peppers = 12 × 6 = $72

✔ Answer: $72

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6. Mr. Jeff divided his money in the ratio 4:2 between Jon and Jack. Jon got the smaller amount of $1,256. How much did Jack receive?

Wait — ratio is 4:2 → simplifies to 2:1
So Jon gets the smaller share → so Jon corresponds to the 2, Jack to 4?

Wait! That contradicts: if Jon got the smaller amount, but 4 > 2, then Jon must be getting the 2 part.

But the ratio is given as 4:2 (Jon:Jack or Jack:Jon?) Let’s read carefully.

It says: "divided his money in the ratio 4:2 between Jon and Jack" and Jon got the smaller amount.

So since Jon got less, he must be the 2 part, and Jack the 4 part.

So:
- Jon : Jack = 2 : 4 → simplified to 1:2
- But the original ratio is 4:2 → which would mean Jon gets 4, Jack gets 2 → that makes Jon get more.

This is a contradiction unless we assume the ratio is Jon:Jack = 4:2, but Jon got the smaller amount → not possible.

So likely, the ratio is Jon:Jack = 2:4 or 4:2 but Jon got the smaller portion → so Jon got 2 parts, Jack got 4 parts.

But it says "ratio 4:2", so let's suppose it's Jon:Jack = 4:2 → Jon gets more → contradicts “Jon got the smaller amount”.

So perhaps the ratio is Jack:Jon = 4:2, or just interpret:

Let total parts = 4 + 2 = 6

If Jon got the smaller amount, then Jon must be the 2 part.

So Jon = 2 parts = $1,256
→ 1 part = 1,256 ÷ 2 = $628
→ Jack = 4 parts = 4 × 628 = $2,512

✔ Answer: Jack received $2,512

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7. 3:4 = 15:20. True OR False?

Check if cross products are equal:
3 × 20 = 60
4 × 15 = 60 → Equal

So yes, equivalent ratios.

✔ Answer: True

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8. 2:5 and 30:20 are equal ratios. True OR False?

Simplify both:

- 2:5 = 2/5
- 30:20 = 3/2 = 1.5

2/5 = 0.4 ≠ 1.5 → Not equal

Alternatively: 2/5 vs 30/20 = 3/2 → Not equal

✔ Answer: False

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9. 3:4 = 6:8? True OR False?

Check:
3/4 = 0.75
6/8 = 0.75 → Equal

Cross multiply: 3×8 = 24, 4×6 = 24 → Equal

✔ Answer: True

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10. 10 glasses cost 40 dollars. How much do 20 glasses cost?

Cost per glass = 40 ÷ 10 = $4
Cost of 20 glasses = 20 × 4 = $80

✔ Answer: $80

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✔ Final Answers Summary:

1. Core: 350 pages, Advanced: 100 pages
2. 21 boys
3. 18 miles = 9 km; 42 km = 84 miles
4. $108
5. $72
6. $2,512
7. True
8. False
9. True
10. $80

Let me know if you'd like these formatted into a printable answer sheet!