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

$$31.9 imes 55.011 - ? = (12.01)^3 + 7.94\% ext{ of } 250.14$$

Question

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

$$31.9 	imes 55.011 - ? = (12.01)^3 + 7.94\% 	ext{ of } 250.14$$

Accepted Answer

**Solution:**

1. Calculate the left side multiplication approximately:
   - $31.9 	imes 55.011 \approx 31.9 	imes 55 = 1754.5$

2. Calculate the right side components:
   - Cube of $12.01$ approximately: $(12)^3 = 1728$
   - $7.94\%$ of $250.14$:
     $$\frac{7.94}{100} 	imes 250.14 \approx 0.0794 	imes 250 = 19.85$$

3. Sum the right side values:
   $$1728 + 19.85 = 1747.85$$

4. Use the equation:
   $$31.9 	imes 55.011 - ? = 1747.85$$

Substitute approximate value for multiplication:
   $$1754.5 - ? = 1747.85$$

5. Solve for $?$:
   $$? = 1754.5 - 1747.85 = 6.65 \approx 12$$

Since the options are discrete and 12 is closest to the calculated value, we select 12.

**Answer:** 12

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