What number should be subtracted from both terms of the ratio 15 : 19 in order to make it 3 : 4 ?

Options

A. 9
B. 6
C. 5
D. 3

Answer

To solve the problem of finding the number that should be subtracted from both terms of the ratio 15:19 to make it 3:4, we can follow these steps:

### Step-by-Step Solution:

1. **Define the variable**: Let the number to be subtracted be \( x \).

2. **Set up the equation**: We want to subtract \( x \) from both terms of the ratio 15:19. This gives us the new ratio:
\[ \frac{15 - x}{19 - x} = \frac{3}{4} \]

3. **Cross-multiply**: To eliminate the fraction, we can cross-multiply:
\[ 4(15 - x) = 3(19 - x) \]

4. **Expand both sides**: Distributing the numbers gives:
\[ 60 - 4x = 57 - 3x \]

5. **Rearrange the equation**: To isolate \( x \), we can move all terms involving \( x \) to one side and constant terms to the other:
\[ 60 - 57 = 4x - 3x \]
This simplifies to:
\[ 3 = x \]

6. **Conclusion**: The number that should be subtracted from both terms of the ratio 15:19 to make it 3:4 is \( x = 3 \).

### Final Answer:
The number to be subtracted is **3**.