Explanation:
Let’s solve each problem one by one, step by step.
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?
We assume the *ratio* of boys to girls stays the same.
Original ratio = boys : girls = 63 : 27
Simplify: divide both by 9 → 63 ÷ 9 = 7, 27 ÷ 9 = 3 → ratio is 7 : 3
So for every 3 girls, there are 7 boys.
Now there are 9 girls. How many groups of 3 girls?
9 ÷ 3 = 3 groups.
Each group corresponds to 7 boys → 3 × 7 =
21 boys.
✔ Check: 21 boys : 9 girls = 21/9 = 7/3 — same as original ratio. ✔️
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Problem 2:
A machine can produce 6 yards of fabric in 2 minutes. How much fabric can it produce in 1 hour?
First, find rate per minute:
6 yards in 2 minutes → 6 ÷ 2 =
3 yards per minute.
1 hour = 60 minutes.
So in 60 minutes: 3 × 60 =
180 yards.
✔ Check: 2 min → 6 yd, so 60 min = 30 × 2 min → 30 × 6 = 180 yd. ✔️
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Problem 3:
12 miles ≈ 19 km. How many km (approx.) are equal to 18 miles?
Set up a proportion:
12 miles → 19 km
18 miles → ? km
Use unit rate:
1 mile ≈ 19 ÷ 12 km = 1.583... km
Then 18 miles ≈ 18 × (19/12) = (18/12) × 19 = (3/2) × 19 = 1.5 × 19 =
28.5 km
Since it says “approx.”, we can write
28.5 km or round to
29 km, but 28.5 is exact from the given ratio. The question says “approx.”, and 12 mi = 19 km is already approximate, so 28.5 is fine.
✔ Check: 12 → 19, so 18 is 1.5×12 → 1.5×19 = 28.5 ✔️
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Problem 4:
80 boys are attending a picnic. Ratio of girls to boys is 3:5. How many girls?
Ratio girls : boys = 3 : 5
That means for every 5 boys, there are 3 girls.
We have 80 boys. How many groups of 5 boys?
80 ÷ 5 = 16 groups.
Each group has 3 girls → 16 × 3 =
48 girls.
✔ Check: 48 girls : 80 boys = divide both by 16 → 3 : 5 ✔️
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Problem 5:
Total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?
Find weight per box:
45 ÷ 15 =
3 pounds per box
Then 40 boxes × 3 =
120 pounds
✔ Check: 15 × 3 = 45, 40 × 3 = 120 ✔️
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Problem 6 (labeled as second #5 — typo in worksheet):
4 spoons cost $12. How much do 16 spoons cost?
Cost per spoon: $12 ÷ 4 = $3 per spoon
16 spoons × $3 =
$48
✔ Check: 4 → $12, so 16 is 4×4 → 4×$12 = $48 ✔️
Final Answer:
1) 21
2) 180
3) 28.5
4) 48
5) 120
6) 48
Parent Tip: Review the logic above to help your child master the concept of ratio and proportion worksheet.
