Ratio and Proportion Word Problems Worksheet 1 with a cartoon farmer and tractor illustration.

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 (Jon:Jack)

But Jon got the smaller amount → so Jon must be the one with the 2 parts? Wait — let’s check:

Actually, ratio 4:2 → Jon:Jack = 4:2 → Jon has more than Jack?

But it says Jon got the smaller amount → contradiction unless the ratio is misassigned.

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

So if Jon got the smaller amount, then Jon must be the one with the 2 part.

So Jon : Jack = 2 : 4 → or simplified 1:2

But the ratio given is 4:2 → which means Jon has 4 parts, Jack has 2 → Jon gets more.

But the problem says Jon got the smaller amount → so this implies that the ratio might be Jack:Jon = 4:2, or perhaps we need to reassign.

Wait — likely typo in interpretation.

But the ratio is 4:2 between Jon and Jack — meaning Jon:Jack = 4:2 → Jon gets more.

But it says Jon got the smaller amount → contradiction.

Unless the ratio is Jack:Jon = 4:2, but the problem says “between Jon and Jack” — order matters.

Wait — perhaps it's Jon:Jack = 4:2, but Jon got the smaller amount? That can’t be.

So either the problem has a mistake, or we misread.

Wait — “Jon got the smaller amount of $1,256” → so Jon received $1,256, and that is the smaller share.

But if the ratio is 4:2, then Jon must be getting 4 parts, Jack 2 → Jon gets more.

So contradiction.

Therefore, the only way this makes sense is if the ratio 4:2 refers to Jack:Jon — i.e., Jack gets 4 parts, Jon gets 2.

But the problem says: "divided his money in the ratio 4:2 between Jon and Jack"

That usually means Jon:Jack = 4:2

But Jon got the smaller amount → impossible.

So maybe the ratio is Jon:Jack = 2:4, but written as 4:2?

Alternatively, maybe the ratio is 4:2, but Jon got the smaller share → so Jon must be the 2 part.

So perhaps the ratio is Jon:Jack = 2:4, but they wrote it as 4:2 by mistake?

But let's assume the ratio is 4:2, and Jon got the smaller amount → then Jon must be the 2 part.

So likely, the ratio is Jon:Jack = 2:4 → or 1:2

But it says 4:2 → so let’s suppose the ratio is Jon:Jack = 2:4, but stated as 4:2 → no.

Alternative: maybe the ratio is 4:2, but Jon got the smaller amount → so Jon must be the 2 part → so the ratio must be Jon:Jack = 2:4 → but they said 4:2.

This suggests that the ratio 4:2 is Jack:Jon, not Jon:Jack.

But the problem says: “divided his money in the ratio 4:2 between Jon and Jack”

Standard interpretation: first number is Jon, second is Jack.

So Jon:Jack = 4:2 → Jon gets more.

But Jon got the smaller amount → contradiction.

So unless Jon got $1,256, and that’s the smaller amount, then Jon must have gotten the 2 part.

So the 2 part = $1,256

Then total parts = 4 + 2 = 6

Each part = 1,256 ÷ 2 = $628

Then Jack gets 4 parts = 4 × 628 = $2,512

So even though the ratio is 4:2, Jon got the 2 part → so Jon is the one with the smaller share.

So the ratio must be Jon:Jack = 2:4 → but written as 4:2? No.

Wait — perhaps the ratio is 4:2, but Jon got the 2 portion → so Jon is the second person → so the ratio is Jack:Jon = 4:2

But the problem says “between Jon and Jack” — so it should be Jon:Jack.

This is confusing.

But let's go with logic:

- Ratio 4:2 → total 6 parts
- Jon got the smaller amount = $1,256 → so Jon got 2 parts
- So each part = 1,256 ÷ 2 = $628
- Jack got 4 parts = 4 × 628 = $2,512

✔ Answer: Jack received $2,512

Even though the ratio is 4:2, and Jon got the smaller amount, it implies Jon got the 2 part → so Jon:Jack = 2:4 → but they wrote 4:2 → possibly a misordering.

But mathematically, we can proceed.

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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 = 0.4
- 30:20 = 30/20 = 3/2 = 1.5 → Not equal

Cross multiply:
2 × 20 = 40
5 × 30 = 150 → Not equal

✔ Answer: False

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

3/4 = 0.75
6/8 = 0.75 → Yes

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
20 glasses = 20 × 4 = $80

✔ Answer: $80

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## ✔ Final Answers:

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 (Jack)
7. True
8. False
9. True
10. $80

Let me know if you'd like these explained further!