Let’s solve each problem one by one, 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 assume the ratio of boys to girls stays the same.
Original ratio:
Boys : Girls = 63 : 27
Simplify that ratio:
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 9 is 3 × 3, we multiply the boy part by 3 too:
7 × 3 = 21
✔ So, 21 boys.
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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 how much it produces per minute:
6 yards ÷ 2 minutes = 3 yards per minute
1 hour = 60 minutes
So, 3 yards/minute × 60 minutes = 180 yards
✔ Answer: 180 yards
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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
Cross-multiply:
(18 × 19) ÷ 12
Calculate 18 × 19:
18 × 20 = 360, minus 18 = 342
Now divide 342 ÷ 12:
12 × 28 = 336
342 - 336 = 6 → so 28.5
✔ Answer: 28.5 km
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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
✔ Answer: 48 girls
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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:
40 × 3 = 120 pounds
✔ Answer: 120 pounds
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Problem 6 (labeled as 5 again):
4 spoons cost $12. How much do 16 spoons cost?
Cost per spoon:
$12 ÷ 4 = $3 per spoon
16 spoons:
16 × $3 = $48
✔ Answer: $48
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Final Answer:
1. 21
2. 180 yards
3. 28.5 km
4. 48
5. 120 pounds
6. $48
Parent Tip: Review the logic above to help your child master the concept of ratios and proportions worksheet 6th grade.
