What number must be added to each term of the ratio 7 : 5 so that it becomes 4 : 3?

Answer

To solve the problem of determining what number must be added to each term of the ratio 7:5 so that it becomes 4:3, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
Let the number to be added be \( x \). We will add \( x \) to both terms of the ratio 7:5. This gives us the new ratio:
\[ \frac{7 + x}{5 + x} \]
We want this ratio to equal \( \frac{4}{3} \).

2. **Create the Equation**:
Set the two ratios equal to each other:
\[ \frac{7 + x}{5 + x} = \frac{4}{3} \]

3. **Cross Multiply**:
To eliminate the fractions, we cross multiply:
\[ 3(7 + x) = 4(5 + x) \]

4. **Distribute**:
Distribute both sides:
\[ 21 + 3x = 20 + 4x \]

5. **Rearrange the Equation**:
To isolate \( x \), rearrange the equation:
\[ 21 - 20 = 4x - 3x \]
This simplifies to:
\[ 1 = x \]

6. **Conclusion**:
Thus, the number that must be added to each term of the ratio 7:5 to make it 4:3 is:
\[ x = 1 \]

7. **Verification**:
To verify, add 1 to both terms of the original ratio:
- New first term: \( 7 + 1 = 8 \)
- New second term: \( 5 + 1 = 6 \)
Now check the new ratio:
\[ \frac{8}{6} = \frac{4}{3} \]
This confirms that our solution is correct.