Calculate the value of $?$ in the equation:

$$96.96 + 996.96 - 99.66 + 999.96 + 5.96 = 399.96 imes ?$$

Question

Calculate the value of $?$ in the equation:

$$96.96 + 996.96 - 99.66 + 999.96 + 5.96 = 399.96 	imes ?$$

Accepted Answer

**Solution:**

1. First, simplify the left-hand side (LHS) of the equation:

$$96.96 + 996.96 - 99.66 + 999.96 + 5.96$$

2. Calculate step-by-step:

- $96.96 + 996.96 = 1093.92$
   - $1093.92 - 99.66 = 994.26$
   - $994.26 + 999.96 = 1994.22$
   - $1994.22 + 5.96 = 2000.18$

3. The equation becomes:

$$2000.18 = 399.96 	imes ?$$

4. To find $?$:

$$? = \frac{2000.18}{399.96}$$

5. Approximate the division:

- $399.96 	imes 5 = 1999.8$
   - $399.96 	imes 6 = 2399.76$

Since $2000.18$ is very close to $1999.8$, $?$ is approximately $5.00095$, but let's check more precisely.

6. Calculate:

$$? = \frac{2000.18}{399.96} \approx 5.00095$$

This is very close to $5$, but the options include $5$ and $8$.

7. Re-examining the initial sum carefully for possible rounding or calculation errors:

Let's add the numbers again:

- $96.96 + 996.96 = 1093.92$
   - $1093.92 - 99.66 = 994.26$
   - $994.26 + 999.96 = 1994.22$
   - $1994.22 + 5.96 = 2000.18$

So the sum is correct.

8. Now, check if $399.96 	imes 5 = 1999.8$ (close to $2000.18$), difference is $0.38$.

9. Check $399.96 	imes 8 = 3199.68$, which is much larger.

10. Check $399.96 	imes 7 = 2799.72$, still too large.

11. Check $399.96 	imes 6 = 2399.76$, still too large.

12. Check $399.96 	imes 4 = 1599.84$, too small.

13. The closest integer multiplier is $5$.

**Answer:** $5$

Answer

Answer

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