How much should be added to each term of 5:6 so that it becomes 2:3 ?

Options

A. a. -3
B. b. 3
C. c. 2
D. d. -2

Answer

To solve the problem of how much should be added to each term of the ratio 5:6 so that it becomes 2:3, we can follow these steps:

### Step-by-Step Solution:

1. **Define the variable**: Let the amount to be added to each term of the ratio 5:6 be denoted as \( x \).

2. **Set up the equation**: When \( x \) is added to both terms of the ratio 5:6, the new ratio becomes:
\[ \frac{5 + x}{6 + x} = \frac{2}{3} \]

3. **Cross-multiply**: To eliminate the fraction, we cross-multiply:
\[ 3(5 + x) = 2(6 + x) \]

4. **Expand both sides**: Distributing the numbers gives us:
\[ 15 + 3x = 12 + 2x \]

5. **Rearrange the equation**: Move all terms involving \( x \) to one side and constant terms to the other side:
\[ 3x - 2x = 12 - 15 \]
This simplifies to:
\[ x = -3 \]

6. **Conclusion**: Therefore, the amount that should be added to each term of the ratio 5:6 to make it 2:3 is \( -3 \). This means that we would actually need to subtract 3 from each term.