Question

A soccer player gets 2 points for a goal and 1 point for an assist. If the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? Assume g represents the number of goals and a represents the number of assists.
g + a = 24. g + 2 a = 42.
g + a = 24. 2 g + a = 42.
g + a = 42. g + 2 a = 24.
g + a = 42. 2 g + a = 24.

Answer 1

To analyze the problem, let's define the variables clearly:

- Let \( g \) represent the number of goals.
- Let \( a \) represent the number of assists.

From the information given, we can establish the following equations:

1. The total number of goals and assists is 24:
\[
g + a = 24
\]

2. The total number of points from goals and assists (2 points for each goal and 1 point for each assist) is 42:
\[
2g + a = 42
\]

Now, we can identify the correct system of equations that represents the situation:

- The first equation is \( g + a = 24 \).
- The second equation is \( 2g + a = 42 \).

Therefore, the correct system of equations that can be used to determine the number of goals and assists is:
\[
g + a = 24
\]
\[
2g + a = 42
\]

Looking at the options provided, the correct option is:
**g + a = 24. 2g + a = 42.**