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
So, 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
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 → simplify: 2:1
But Jon got the
smaller amount, so Jon must be the one who got the "2" part?
No — wait: 4:2 → Jon got the smaller amount ($1,256), so Jon must have received the
2 part.
So:
- 2 parts = $1,256
- 1 part = 1,256 ÷ 2 = $628
- Jack got 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
Yes, equal →
True
✔ Answer: True
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8. 2:5 and 30:20 are equal ratios. True OR False?
Simplify both:
- 2:5 → already simplified
- 30:20 = 3:2 (divide both by 10)
2:5 ≠ 3:2 →
False
✔ Answer: False
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9. 3:4 = 6:8? True OR False?
Check cross products:
3 × 8 = 24
4 × 6 = 24 → Equal
So, yes →
True
✔ 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 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 this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of math word problems with ratios.
