Find the number that must be added to the terms of the ratio 7 : 13 to make it equal to 2:3.

Options

A. 5
B. 7
C. 4
D. 6

Answer

To solve the problem of finding the number that must be added to the terms of the ratio 7:13 to make it equal to 2:3, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Unknown**:
Let the number to be added be \( A \).

2. **Set Up the Equation**:
After adding \( A \) to both terms of the ratio 7:13, the new ratio becomes \( \frac{7 + A}{13 + A} \). We want this to equal the ratio \( \frac{2}{3} \).

So, we can write the equation:
\[ \frac{7 + A}{13 + A} = \frac{2}{3} \]

3. **Cross Multiply**:
To eliminate the fractions, we cross-multiply:
\[ 3(7 + A) = 2(13 + A) \]

4. **Expand Both Sides**:
Expanding both sides gives:
\[ 21 + 3A = 26 + 2A \]

5. **Rearrange the Equation**:
To isolate \( A \), we can rearrange the equation:
\[ 3A - 2A = 26 - 21 \]
This simplifies to:
\[ A = 5 \]

6. **Conclusion**:
The number that must be added to the terms of the ratio 7:13 to make it equal to 2:3 is \( 5 \).

### Final Answer:
The required number is \( 5 \).

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