Question
Bryce had a $25 gift card to use on songs and games at an online media store. Songs cost $2 each and games cost $5 each. Bryce spent all the money on the gift card to download 8 items. Solve the system to determine how many games he purchased. Let s represent the number of songs and g represent the number of games.
s + g = 8
2s + 5g = 25
Bryce purchased
games.
s + g = 8
2s + 5g = 25
Bryce purchased
games.
Answers
GPT-4o mini
To solve the system of equations given by:
1. \( s + g = 8 \)
2. \( 2s + 5g = 25 \)
where \( s \) represents the number of songs and \( g \) represents the number of games, we can use the first equation to express \( s \) in terms of \( g \):
\[
s = 8 - g
\]
Now, we can substitute this expression for \( s \) into the second equation:
\[
2(8 - g) + 5g = 25
\]
Distributing the 2 gives:
\[
16 - 2g + 5g = 25
\]
Combining like terms results in:
\[
16 + 3g = 25
\]
Now, subtract 16 from both sides:
\[
3g = 9
\]
Next, divide by 3:
\[
g = 3
\]
Now that we've found \( g \), let's find \( s \) using the first equation:
\[
s + 3 = 8 \implies s = 5
\]
Thus, Bryce purchased:
- \( s = 5 \) songs
- \( g = 3 \) games
So, Bryce purchased **3 games**.
1. \( s + g = 8 \)
2. \( 2s + 5g = 25 \)
where \( s \) represents the number of songs and \( g \) represents the number of games, we can use the first equation to express \( s \) in terms of \( g \):
\[
s = 8 - g
\]
Now, we can substitute this expression for \( s \) into the second equation:
\[
2(8 - g) + 5g = 25
\]
Distributing the 2 gives:
\[
16 - 2g + 5g = 25
\]
Combining like terms results in:
\[
16 + 3g = 25
\]
Now, subtract 16 from both sides:
\[
3g = 9
\]
Next, divide by 3:
\[
g = 3
\]
Now that we've found \( g \), let's find \( s \) using the first equation:
\[
s + 3 = 8 \implies s = 5
\]
Thus, Bryce purchased:
- \( s = 5 \) songs
- \( g = 3 \) games
So, Bryce purchased **3 games**.