Question

Avery randomly selects 50 colored pencils from a basket and finds that 2 are not sharpened. If the basket contains 300 colored pencils, how many would you expect to be unsharpened?

*Hint: Write a proportion*

(1 point)
Responses

2
2

12
12

20
20

100

Answer 1

To solve this problem, we can use a proportion to estimate how many unsharpened pencils are in the entire basket based on the sample Avery selected.

First, we need to determine the proportion of unsharpened pencils in the sample:

- Avery selected 50 pencils, and 2 of them were not sharpened.
- Therefore, the proportion of unsharpened pencils in the sample is \( \frac{2}{50} \).

Now, let's set up a proportion to find out how many unsharpened pencils we expect in the entire basket of 300 pencils. Let \( x \) be the number of unsharpened pencils in the total of 300 pencils.

We can set up the equation:

\[
\frac{2}{50} = \frac{x}{300}
\]

To solve for \( x \), we can cross-multiply:

\[
2 \cdot 300 = 50 \cdot x
\]

This simplifies to:

\[
600 = 50x
\]

Now, divide both sides by 50:

\[
x = \frac{600}{50} = 12
\]

Therefore, based on the proportion, we would expect **12 unsharpened colored pencils** in the basket.

The correct response is:

**12**