If $9.99\%$ of $299.99$ equals $x^3 + y$, where $x$ and $y$ are integers, what is the value of $x$?

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**Solution:**

1. Calculate $9.99\%$ of $299.99$:
   
   $$9.99\% 	imes 299.99 = \frac{9.99}{100} 	imes 299.99$$

2. Multiply the numbers:

$$= 0.0999 	imes 299.99 \approx 29.97$$

3. The expression is given as $x^3 + y$, where $x$ and $y$ are integers. We need to find integers $x$ and $y$ such that:

$$x^3 + y = 29.97 \approx 30$$

4. Check cubes near 30:

- $3^3 = 27$, so $y = 30 - 27 = 3$
   - $4^3 = 64$ (too large)
   - $5^3 = 125$ (too large)

5. Therefore, $x = 3$ and $y = 3$ satisfy the equation approximately.

6. However, the question asks for the value of $x$.

**Answer:** $3$

**Note:** The closest integer cube root to the value is $3$, so $x = 3$.

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