Question

Aspen scored a minimum of 18 points in her last basketball game. She scored 6 points on free throws that are worth 1 point each. The rest of the points she scored on 3-point shots.
Which inequality can be used to determine, p, the number of 3-point shots that Aspen made? 7.PAFR.2.1
1. 3p+6>18
2. 3p+6<18
3. 3p+6≥18
4. 3p+6≤18

Answer 1

To determine the correct inequality for the situation described, we can break it down step by step:

- Aspen scored a minimum of 18 points.
- She scored 6 points from free throws (which are worth 1 point each).
- The rest of her points were scored from 3-point shots.

Let \( p \) be the number of 3-point shots. Each 3-point shot is worth 3 points, so the points from 3-point shots can be represented as \( 3p \).

The total points scored by Aspen can be expressed as:

\[
\text{Total Points} = \text{Points from Free Throws} + \text{Points from 3-Point Shots}
\]
\[
\text{Total Points} = 6 + 3p
\]

Since she scored at least 18 points, we need to set up the inequality:

\[
6 + 3p \geq 18
\]

To find the appropriate option from the given choices, let's simplify this inequality step by step:

1. Subtract 6 from both sides:
\[
3p \geq 18 - 6
\]
\[
3p \geq 12
\]

Thus, the correct inequality that can be used to determine \( p \), the number of 3-point shots that Aspen made, is:

\[
3p + 6 \geq 18
\]

So, the answer is:

**3. \( 3p + 6 \geq 18 \)**