If 3/5 of P = 4/5 of Q, then what is P : Q?

Options

A. ` 4 : 3 `
B. ` 4 : 7 `
C. ` 4 : 9 `
D. `2 : 5 `

Answer

To solve the problem "If \( \frac{3}{5} P = \frac{4}{5} Q \), then what is \( P : Q \)?", we can follow these steps:

### Step-by-step Solution:

1. **Start with the given equation**:
\[ \frac{3}{5} P = \frac{4}{5} Q \]

2. **Eliminate the fractions**:
To eliminate the fractions, we can multiply both sides of the equation by 5:
\[ 5 \cdot \frac{3}{5} P = 5 \cdot \frac{4}{5} Q \]
This simplifies to:
\[ 3P = 4Q \]

3. **Rearrange the equation**:
We want to express \( P \) in terms of \( Q \). To do this, we can divide both sides by \( Q \) and also divide by 3:
\[ \frac{P}{Q} = \frac{4}{3} \]

4. **Express the ratio**:
From the equation \( \frac{P}{Q} = \frac{4}{3} \), we can express the ratio \( P : Q \) as:
\[ P : Q = 4 : 3 \]

### Final Answer:
Thus, the ratio \( P : Q \) is \( 4 : 3 \).

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