Let’s solve each problem one by one.
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Problem 1:
A playschool has 63 boys and 27 girls. What will be the number of boys if there are 9 girls in the school?
→ First, find the ratio of boys to girls:
63 boys : 27 girls → divide both by 9 → 7 : 3
So for every 3 girls, there are 7 boys.
If there are 9 girls, that’s 3 × 3 = 9 → so multiply boys part by 3 too:
7 × 3 =
21 boys
✔ Check: 21 boys / 9 girls = 7/3 → same as original ratio. Good.
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Problem 2:
A machine can produce 6 yards of fabric in 2 minutes. How much fabric can the machine produce in 1 hour?
→ 1 hour = 60 minutes
In 2 minutes → 6 yards
So in 1 minute → 6 ÷ 2 = 3 yards
In 60 minutes → 3 × 60 =
180 yards
✔ Check: 6 yards per 2 min → 3 yards per min → 180 in 60 min. Correct.
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Problem 3:
12 miles are approximately equal to 19 km. How many km (approx.) are equal to 18 miles?
→ Set up proportion:
12 miles → 19 km
18 miles → ? km
Cross-multiply:
(18 × 19) ÷ 12 = ?
First, 18 ÷ 12 = 1.5
Then 1.5 × 19 = 28.5
Or: 18 × 19 = 342; 342 ÷ 12 = 28.5
✔ So answer is
28.5 km
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Problem 4:
80 boys are attending a picnic. There is a ratio of 3:5 for the number of girls to the number of boys. How many girls are there?
→ Ratio girls : boys = 3 : 5
Boys = 80 → which corresponds to 5 parts
So 1 part = 80 ÷ 5 = 16
Girls = 3 parts → 3 × 16 =
48 girls
✔ Check: 48 girls : 80 boys → divide both by 16 → 3:5. Correct.
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Problem 5:
The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?
→ Weight per box = 45 ÷ 15 = 3 pounds
40 boxes → 40 × 3 =
120 pounds
✔ Check: 15 boxes = 45 lbs → 1 box = 3 lbs → 40 × 3 = 120. Correct.
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Problem 6 (labeled as second “5”):
4 spoons cost $12. How much do 16 spoons cost?
→ Cost per spoon = 12 ÷ 4 = $3
16 spoons → 16 × 3 =
$48
✔ Check: 4 spoons = $12 → 16 is 4 times more → 12 × 4 = 48. Correct.
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Final Answer:
1. 21
2. 180 yards
3. 28.5 km
4. 48 girls
5. 120 pounds
6. $48
Parent Tip: Review the logic above to help your child master the concept of proportion worksheet 6th grade.
