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

Sure! Let’s solve each problem step by step with clear explanations.

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Problem 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?*

✔ Solution:
The ratio 7:2 means for every 7 parts core, there are 2 parts advanced.
Total parts = 7 + 2 = 9 parts.
Each part = 450 ÷ 9 = 50 pages.

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

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

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Problem 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?*

✔ Solution:
Ratio girls:boys = 3:7 → total parts = 3 + 7 = 10 parts.
Total people = 30 → each part = 30 ÷ 10 = 3.

Boys = 7 parts × 3 = 21 boys

✔️ Answer: 21 boys

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Problem 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?*

✔ Solution:
First, find the conversion rate:
12 miles = 6 km → so 1 mile = 6 ÷ 12 = 0.5 km

→ 18 miles = 18 × 0.5 = 9 km

Now reverse:
Since 6 km = 12 miles → 1 km = 12 ÷ 6 = 2 miles

→ 42 km = 42 × 2 = 84 miles

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

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

✔ Solution:
Cost per pizza = 60 ÷ 5 = $12
Cost for 9 pizzas = 9 × 12 = $108

✔️ Answer: $108

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

✔ Solution:
Cost per pepper = 36 ÷ 6 = $6
Cost for 12 = 12 × 6 = $72

✔️ Answer: $72

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Problem 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?*

✔ Solution:
Ratio Jon:Jack = 4:2 → but wait — Jon got the *smaller* amount? That doesn’t match unless we switch them.

Actually, if Jon got the smaller amount, then the ratio must be Jack:Jon = 4:2, meaning Jack gets more.

So let’s assume the ratio given is Jack : Jon = 4 : 2 (since Jon got less).

Simplify ratio: 4:2 = 2:1 → So Jack gets twice what Jon gets.

Jon = $1,256 → Jack = 2 × 1,256 = $2,512

✔️ Answer: Jack received $2,512

*(Note: The wording says “divided his money in the ratio 4:2 between Jon and Jack” and “Jon got the smaller amount.” So logically, Jon corresponds to 2 parts, Jack to 4 parts.)*

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

✔ Solution:
Check if ratios are equivalent:
3/4 = ? 15/20 → 15/20 simplifies to 3/4 (divide numerator and denominator by 5).
So yes, they are equal.

✔️ Answer: True

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

✔ Solution:
2:5 = 2/5 = 0.4
30:20 = 30/20 = 3/2 = 1.5
0.4 ≠ 1.5 → Not equal.

✔️ Answer: False

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

✔ Solution:
3/4 = 0.75
6/8 = 0.75 → Same value.

✔️ Answer: True

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

✔ Solution:
Cost per glass = 40 ÷ 10 = $4
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

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