Increase 224 in the ratio 7 : 9

Answer

To solve the problem of increasing 224 in the ratio of 7:9, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The ratio 7:9 indicates that for every 7 parts of the original value, we want to find the corresponding 9 parts of the new value.

2. **Set Up the Equation**: We can express the relationship between the new value (let's call it \( x \)) and the old value (224) using the ratio:
\[ \frac{x}{224} = \frac{7}{9} \]

3. **Cross-Multiply**: To eliminate the fraction, we can cross-multiply:
\[ 9x = 7 \times 224 \]

4. **Calculate the Right Side**: Now, calculate \( 7 \times 224 \):
\[ 7 \times 224 = 1568 \]
So, the equation now looks like:
\[ 9x = 1568 \]

5. **Solve for \( x \)**: To find \( x \), divide both sides by 9:
\[ x = \frac{1568}{9} \]

6. **Perform the Division**: Now, calculate \( \frac{1568}{9} \):
\[ x = 174.2222\ldots \approx 174.22 \]

7. **Final Answer**: Thus, the new value when increasing 224 in the ratio 7:9 is approximately:
\[ x \approx 174.22 \]