Find the value of $x$ if

$$x \% ext{ of } 24.91\% ext{ of } 39.93\% ext{ of } \left((11.93)^2 + 5.98 ight) = 2.25$$

Question

Find the value of $x$ if

$$x \% 	ext{ of } 24.91\% 	ext{ of } 39.93\% 	ext{ of } \left((11.93)^2 + 5.98ight) = 2.25$$

Accepted Answer

**Solution:**

1. First, calculate the value inside the parentheses:
   $$ (11.93)^2 + 5.98 = 142.3249 + 5.98 = 148.3049 $$

2. Calculate the successive percentages:
   - $24.91\%$ of $39.93\%$ of $148.3049$
   
   Convert percentages to decimals:
   $$ 24.91\% = 0.2491, \quad 39.93\% = 0.3993 $$

Calculate:
   $$ 0.2491 	imes 0.3993 = 0.09944 $$

Then multiply by $148.3049$:
   $$ 0.09944 	imes 148.3049 \approx 14.75 $$

3. Now, the equation becomes:
   $$ x\% 	ext{ of } 14.75 = 2.25 $$

Converting $x\%$ to decimal form:
   $$ \frac{x}{100} 	imes 14.75 = 2.25 $$

4. Solve for $x$:
   $$ \frac{x}{100} = \frac{2.25}{14.75} \implies x = \frac{2.25}{14.75} 	imes 100 $$

Calculate:
   $$ x \approx 15.25 $$

5. Among the given options, the closest value to $15.25$ is $18$ (since $15$ is less and $18$ is the nearest higher option). However, rechecking the decimal multiplication for accuracy:

Recalculate step 2 precisely:
   $$ 0.2491 	imes 0.3993 = 0.09944 $$ (correct)

$$ 0.09944 	imes 148.3049 = 14.75 $$ (correct)

Step 4:
   $$ x = \frac{2.25}{14.75} 	imes 100 = 15.25 $$

So the exact value is approximately $15.25$, which is closest to option (d) $15$.

**Answer:** $15$

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