Printable math worksheet titled "Ratio and Proportion Worksheet" featuring six word problems related to real-world applications of ratios and proportions.

Let's solve each problem step by step using ratio and proportion concepts.

---

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?

#### Step 1: Find the ratio of boys to girls.
$$
\text{Ratio of boys to girls} = \frac{63}{27} = \frac{7}{3} \quad \text{(simplify by dividing both by 9)}
$$

So, for every 3 girls, there are 7 boys.

Now, we want to find how many boys there are when there are 9 girls.

Set up a proportion:
$$
\frac{7}{3} = \frac{x}{9}
$$

Cross-multiply:
$$
7 \times 9 = 3x \Rightarrow 63 = 3x \Rightarrow x = 21
$$

✔ 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?

#### Step 1: Convert 1 hour to minutes.
$$
1 \text{ hour} = 60 \text{ minutes}
$$

#### Step 2: Find rate of production per minute.
$$
\text{In 2 minutes} \rightarrow 6 \text{ yards} \\
\text{So in 1 minute} \rightarrow \frac{6}{2} = 3 \text{ yards}
$$

#### Step 3: Multiply by 60 minutes.
$$
3 \text{ yards/minute} \times 60 = 180 \text{ yards}
$$

✔ 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:
$$
12x = 19 \times 18 = 342 \\
x = \frac{342}{12} = 28.5
$$

✔ 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?

The ratio girls : boys = 3 : 5

Let number of girls = $3x$, number of boys = $5x$

But we know boys = 80:
$$
5x = 80 \Rightarrow x = 16
$$

So, number of girls = $3x = 3 \times 16 = 48$

✔ Answer: 48 girls

---

Problem 5

The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?

First, find weight of one box:
$$
\frac{45 \text{ pounds}}{15 \text{ boxes}} = 3 \text{ pounds per box}
$$

Now, 40 boxes:
$$
40 \times 3 = 120 \text{ pounds}
$$

✔ Answer: 120 pounds

---

Problem 6

4 spoons cost $12. How much do 16 spoons cost?

Find cost per spoon:
$$
\frac{12}{4} = 3 \text{ dollars per spoon}
$$

Now, 16 spoons:
$$
16 \times 3 = 48 \text{ dollars}
$$

✔ Answer: $48

---

✔ Final Answers:

1. 21 boys
2. 180 yards
3. 28.5 km
4. 48 girls
5. 120 pounds
6. $48

Let me know if you'd like these explained visually or with diagrams!