Ratio and Proportions Word Problem Packet | PDF | Ratio | Teaching ... - Free Printable

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 got the smaller share, which corresponds to the 2 part?

Wait — actually, let’s clarify:

If the ratio is 4:2, then:
- Jon gets 4 parts
- Jack gets 2 parts

But it says Jon got the smaller amount, so that contradicts unless we misassigned.

Wait — this is important.

The ratio is 4:2, but Jon got the smaller amount.

So if Jon got less, then Jon must be the one who got the 2 parts, and Jack got 4 parts.

So likely, the ratio is Jon:Jack = 2:4, or 1:2, but the problem says "divided in the ratio 4:2 between Jon and Jack", and Jon got the smaller amount.

That means the ratio must be Jon:Jack = 2:4 (since 2 is smaller), but it says 4:2.

Ah! This implies that the ratio is 4:2, and Jon got the smaller amount, so Jon must be the one getting 2 parts, and Jack got 4 parts.

So maybe the ratio is Jon:Jack = 2:4, but written as 4:2? That would be backwards.

Wait — probably the ratio is 4:2, and Jon got the smaller amount, so Jon got 2 parts, and Jack got 4 parts.

But that would mean the ratio is Jon:Jack = 2:4, i.e., simplified to 1:2.

But the problem says "divided in the ratio 4:2 between Jon and Jack" — so likely Jon:Jack = 4:2, but then Jon should get more.

But the problem says Jon got the smaller amount — contradiction.

So either:
- The ratio is 4:2, but Jon got the smaller amount → impossible unless Jon is the one getting 2 parts.
- So perhaps the ratio is Jon:Jack = 2:4, but labeled as 4:2?

This is confusing.

But the key sentence: "Jon got the smaller amount of $1,256"

So Jon received $1,256, and it's the smaller share.

Now, ratio is 4:2 → total parts = 6

Let’s suppose the ratio is Jon:Jack = 4:2, then Jon gets more → contradiction.

So instead, the ratio must be Jon:Jack = 2:4 → Jon gets 2 parts, Jack gets 4 parts.

But the problem says "divided in the ratio 4:2 between Jon and Jack" — so perhaps it's Jon:Jack = 2:4, and they wrote it as 4:2? No, that doesn't make sense.

Wait — maybe the ratio is 4:2, but Jon got the smaller portion, so Jon got 2 parts, Jack got 4 parts.

So the ratio is Jon:Jack = 2:4, but stated as 4:2? That would be backward.

Alternatively, perhaps the ratio is 4:2, and Jon got 2 parts, Jack got 4 parts — so Jon got less.

Then the ratio is Jon:Jack = 2:4, but the problem says "divided in the ratio 4:2 between Jon and Jack" — which might mean Jon:Jack = 4:2, but that would make Jon get more.

This is inconsistent.

Wait — maybe the ratio is 4:2, and Jon got the smaller amount, so Jon must be the one getting the 2 part.

So the ratio Jon:Jack = 2:4, but the problem says "in the ratio 4:2" — perhaps it's a typo?

But let's assume the ratio is 4:2, and Jon got the smaller amount, so Jon must be the one receiving 2 parts, Jack 4 parts.

So the ratio is Jon:Jack = 2:4, but written as 4:2 — that can’t be.

Wait — unless the ratio is 4:2, and Jon got the 2-part share, so Jon = 2 parts = $1,256

Then each part = 1,256 ÷ 2 = $628

Jack got 4 parts = 4 × 628 = $2,512

Yes — that works.

So even though the ratio is given as 4:2, and Jon got the smaller amount, it means Jon got 2 parts, Jack got 4 parts.

So total parts = 6

Jon = 2 parts = $1,256 → 1 part = $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:
3/4 = 0.75
15/20 = 0.75 → Yes, equal

Cross-multiply: 3×20 = 60, 4×15 = 60 → equal

✔ Answer: True

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

2:5 = 2/5 = 0.4
30:20 = 30/20 = 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 → 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
20 glasses = 20 × 4 = $80

Or use proportion:
10 / 40 = 20 / x → cross-multiply: 10x = 800 → x = 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
7. True
8. False
9. True
10. $80

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