Find the approximate value to replace the question mark (?) in the following expression:

$$\frac{189.97 imes 48.03}{\frac{1368.02}{440.98}} + 86.99\% ext{ of } 500.01 = ?^3$$

Question

Find the approximate value to replace the question mark (?) in the following expression:

$$\frac{189.97 	imes 48.03}{\frac{1368.02}{440.98}} + 86.99\% 	ext{ of } 500.01 = ?^3$$

Accepted Answer

**Solution:**

1. First, approximate the values for easier calculation:
   - $189.97 \approx 190$
   - $48.03 \approx 48$
   - $1368.02 \approx 1368$
   - $440.98 \approx 441$
   - $86.99\% \approx 87\%$
   - $500.01 \approx 500$

2. Calculate the numerator of the fraction:
   $$190 	imes 48 = 9120$$

3. Calculate the denominator of the fraction:
   $$\frac{1368}{441} \approx 3.1$$

4. Divide numerator by denominator:
   $$\frac{9120}{3.1} \approx 2941.94$$

5. Calculate $87\%$ of $500$:
   $$0.87 	imes 500 = 435$$

6. Add the two results:
   $$2941.94 + 435 = 3376.94$$

7. The expression equals $?^3$, so find the cube root of $3376.94$:
   - $15^3 = 3375$

8. Since $3376.94$ is very close to $3375$, the approximate value of $?$ is $15$.

**Answer:** $15$

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