What least number must be subtracted from each term of the ratio `15 : 19` to me the ratio `3 : 4` ?

Options

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

Answer

To solve the problem of finding the least number that must be subtracted from each term of the ratio \(15 : 19\) to make it equal to the ratio \(3 : 4\), we can follow these steps:

### Step-by-Step Solution:

1. **Let the number to be subtracted be \(x\)**:
We denote the number that we need to subtract from both terms of the ratio as \(x\).

2. **Set up the equation**:
After subtracting \(x\) from both terms of the ratio \(15 : 19\), we have:
\[ \frac{15 - x}{19 - x} = \frac{3}{4} \]

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

4. **Distribute on both sides**:
Expanding both sides gives:
\[ 60 - 4x = 57 - 3x \]

5. **Rearrange the equation**:
We want to isolate \(x\). First, we can add \(4x\) to both sides:
\[ 60 = 57 + x \]
Now, subtract \(57\) from both sides:
\[ 60 - 57 = x \]
This simplifies to:
\[ x = 3 \]

6. **Conclusion**:
The least number that must be subtracted from each term of the ratio \(15 : 19\) to make it \(3 : 4\) is \(3\).