Math worksheet titled "Ratio and Proportion Worksheet" featuring five problems related to ratios, proportions, and unit conversions, including scenarios involving boys and girls, fabric production, distance conversion, picnic attendance, box weights, and spoon costs.

Let’s solve each problem step by step.

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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?

We need to keep the ratio of boys to girls the same.

Original ratio:
Boys : Girls = 63 : 27
Simplify: divide both by 9 → 7 : 3

So for every 3 girls, there are 7 boys.

Now, if there are 9 girls, how many boys?

Since 3 girls → 7 boys,
then 9 girls = 3 × 3 girls → 3 × 7 = 21 boys

✔ Check: 21 : 9 = divide by 3 → 7 : 3 — same as original. ✔️

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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?

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 ⇒ 60 min is 30 times longer → 6 × 30 = 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 round to nearest whole number: 29 km, but 28.5 is exact from the given ratio. Usually in such problems, they expect 28.5 or maybe 29. Let's keep 28.5 unless told to round.

But let’s double-check:
12 mi : 19 km = 18 mi : x km
Cross-multiply: 12x = 18 × 19 = 342
x = 342 ÷ 12 = 28.5 ✔️

So answer: 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
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 : 80 = divide by 16 → 3 : 5 ✔️

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Problem 5:
The 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: 40 × 3 = 120 pounds

✔ Check: 15 × 3 = 45, so 40 × 3 = 120 ✔️

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Problem 6 (labeled as second 5 — likely a typo, should be #6):
4 spoons cost $12. How much do 16 spoons cost?

Cost per spoon: $12 ÷ 4 = $3 per spoon
16 spoons: 16 × $3 = $48

✔ Check: 4 spoons = $12 → 16 spoons = 4 × 4 spoons → 4 × $12 = $48 ✔️

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Now compile all final answers in order:

1. 21
2. 180
3. 28.5
4. 48
5. 120
6. 48

Final Answer:
21
180
28.5
48
120
48