Question: Kathryn needs 200 pencils to supply an art project at a local school. They can be purchased in boxes of 32.
If $x$ is the number of boxes that need to be purchased, which equation would be used to solve for $x$?
$32x = 200$
$\frac{x}{32} = 200$
$\frac{x}{200} = 32$
$200x = 32$
1. **State the problem:** Kathryn needs 200 pencils and each box contains 32 pencils. We want to find the number of boxes $x$ needed.
2. **Formula:** The total pencils is the number of boxes times pencils per box, so:
$$32x = 200$$
3. **Explanation:** This equation means the number of boxes $x$ multiplied by 32 pencils per box equals 200 pencils needed.
4. **Check other options:**
- $\frac{x}{32} = 200$ means boxes divided by 32 equals 200, which is incorrect.
- $\frac{x}{200} = 32$ means boxes divided by 200 equals 32, which is incorrect.
- $200x = 32$ means 200 times boxes equals 32, which is incorrect.
5. **Conclusion:** The correct equation to solve for $x$ is:
$$32x = 200$$