Here is the step-by-step solution to each problem on the worksheet:
---
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?*
This is a proportion problem. The ratio of boys to girls remains constant.
Original ratio:
Boys : Girls = 63 : 27
Simplify the ratio by dividing both numbers by 9:
63 ÷ 9 = 7
27 ÷ 9 = 3
→ So,
boys : girls = 7 : 3
Now, if there are 9 girls, we set up a proportion:
Let *x* = number of boys when there are 9 girls.
\[
\frac{7}{3} = \frac{x}{9}
\]
Cross-multiply:
3x = 7 × 9
3x = 63
x = 63 ÷ 3
x = 21
✔ Answer: 21 boys
---
Problem 2:
*A machine can produce 6 yards of fabric in 2 minutes. How much fabric can the machine produce in 1 hour?*
First, convert 1 hour to minutes:
1 hour = 60 minutes
Set up a proportion:
In 2 minutes → 6 yards
In 60 minutes → ? yards
\[
\frac{6 \text{ yards}}{2 \text{ min}} = \frac{x \text{ yards}}{60 \text{ min}}
\]
Cross-multiply:
2x = 6 × 60
2x = 360
x = 360 ÷ 2
x = 180
✔ Answer: 180 yards
---
Problem 3:
*12 miles are approximately equal to 19 km. How many km (approx.) are equal to 18 miles?*
Set up a proportion:
\[
\frac{12 \text{ miles}}{19 \text{ km}} = \frac{18 \text{ miles}}{x \text{ km}}
\]
Cross-multiply:
12x = 19 × 18
12x = 342
x = 342 ÷ 12
x = 28.5
✔ Answer: 28.5 km
---
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 of girls : boys = 3 : 5
That means for every 5 boys, there are 3 girls.
We know there are 80 boys.
Set up proportion:
\[
\frac{3}{5} = \frac{x}{80}
\]
Cross-multiply:
5x = 3 × 80
5x = 240
x = 240 ÷ 5
x = 48
✔ Answer: 48 girls
---
Problem 5 (first one):
*The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?*
Find the weight per box first:
45 pounds ÷ 15 boxes =
3 pounds per box
Now multiply by 40 boxes:
3 × 40 =
120 pounds
✔ Answer: 120 pounds
---
Problem 5 (second one — likely meant to be #6):
*4 spoons cost $12. How much do 16 spoons cost?*
Find cost per spoon:
$12 ÷ 4 spoons =
$3 per spoon
Now multiply by 16 spoons:
3 × 16 =
$48
✔ Answer: $48
---
✔ Final Answers:
1.
21 boys
2.
180 yards
3.
28.5 km
4.
48 girls
5.
120 pounds
6.
$48
*(Note: The worksheet lists two Problem 5s — the second should probably be Problem 6.)*
Parent Tip: Review the logic above to help your child master the concept of ratio and proportions worksheet.
