What is the approximate value that will replace the question mark (?) in the following expression?

$$59.90\% ext{ of } 1020.11 - 9.88\% ext{ of } 79.91 = ?^3 + 92.01$$

Question

What is the approximate value that will replace the question mark (?) in the following expression?

$$59.90\% 	ext{ of } 1020.11 - 9.88\% 	ext{ of } 79.91 = ?^3 + 92.01$$

Accepted Answer

**Solution:**

1. Calculate approximately $59.90\%$ of $1020.11$:
   - $60\%$ of $1020$ is about $0.60 	imes 1020 = 612$
   - Since $59.90\%$ is slightly less than $60\%$, the value is approximately $611$

2. Calculate approximately $9.88\%$ of $79.91$:
   - $10\%$ of $80$ is $8$
   - $9.88\%$ is slightly less than $10\%$, and $79.91$ is slightly less than $80$, so approximately $7.9$

3. Subtract the two values:
   - $611 - 7.9 = 603.1$

4. Now the equation is:
   $$603.1 = ?^3 + 92.01$$

5. Subtract $92.01$ from both sides:
   - $603.1 - 92.01 = 511.09$

6. So,
   $$?^3 = 511.09$$

7. Find the cube root of $511.09$:
   - $8^3 = 512$
   - Since $511.09$ is very close to $512$, $?$ is approximately $8$

**Answer:** $8$

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