What quantity must be subtracted from each term of the ratio `9 : 17` to make it equal to `1 : 3`?

Answer

To solve the problem of finding what quantity must be subtracted from each term of the ratio \(9 : 17\) to make it equal to \(1 : 3\), we can follow these steps:

### Step-by-Step Solution:

1. **Let the quantity to be subtracted be \(x\)**:
We need to find a value \(x\) such that when it is subtracted from both terms of the ratio \(9 : 17\), the new ratio equals \(1 : 3\).

\[ \text{Let } x \text{ be the quantity to be subtracted.} \]

2. **Set up the equation**:
After subtracting \(x\) from both terms of the ratio \(9 : 17\), the new ratio will be:

\[ \frac{9 - x}{17 - x} = \frac{1}{3} \]

3. **Cross-multiply to eliminate the fraction**:
To solve the equation, we can cross-multiply:

\[ 3(9 - x) = 1(17 - x) \]

This simplifies to:

\[ 27 - 3x = 17 - x \]

4. **Rearrange the equation**:
Move all terms involving \(x\) to one side and constant terms to the other side:

\[ 27 - 17 = 3x - x \]

This simplifies to:

\[ 10 = 2x \]

5. **Solve for \(x\)**:
Divide both sides by 2 to find the value of \(x\):

\[ x = \frac{10}{2} = 5 \]

### Final Answer:
The quantity that must be subtracted from each term of the ratio \(9 : 17\) to make it equal to \(1 : 3\) is \(5\).

---