If `3/4=x/28=y/32`, then the values of x and y respectively are _________ and _________.

Options

A. 21, 24
B. 21, 28
C. 18, 24
D. 21, 25

Answer

To solve the problem \( \frac{3}{4} = \frac{x}{28} = \frac{y}{32} \), we will find the values of \( x \) and \( y \) step by step.

### Step 1: Set up the equations
From the given fractions, we can create two equations:
1. \( \frac{3}{4} = \frac{x}{28} \)
2. \( \frac{3}{4} = \frac{y}{32} \)

### Step 2: Solve for \( x \)
Using the first equation \( \frac{3}{4} = \frac{x}{28} \):
- Cross-multiply to eliminate the fractions:
\[ 3 \times 28 = 4 \times x \]
- Calculate \( 3 \times 28 \):
\[ 84 = 4x \]
- Now, divide both sides by 4 to solve for \( x \):
\[ x = \frac{84}{4} = 21 \]

### Step 3: Solve for \( y \)
Using the second equation \( \frac{3}{4} = \frac{y}{32} \):
- Cross-multiply again:
\[ 3 \times 32 = 4 \times y \]
- Calculate \( 3 \times 32 \):
\[ 96 = 4y \]
- Now, divide both sides by 4 to solve for \( y \):
\[ y = \frac{96}{4} = 24 \]

### Final Answer
The values of \( x \) and \( y \) respectively are \( 21 \) and \( 24 \).

---