Question
The Lincoln High School Student Council wants to raise $300 to make a donation to a homeless shelter. To help the students earn the money, the principal has agreed to pay $15 for each member who picks up litter outside, p, and $10 for each member who cleans the hallways, c. All 25 members of the student council will be participating. Write the pair of linear equations that model this situation.(1 point) Responses p+c=300; 10p+15c=25 p+c=300; 10p+15c=25 p+c=300; 15p+10c=25 p+c=300; 15p+10c=25 p+c=25; 10p+15c=300 p+c=25; 10p+15c=300 p+c=25; 15p+10c=300 p+c=25; 15p+10c=300
Answers
GPT-4o mini
To write the pair of linear equations modeling the situation, we need to consider the following:
1. **Total Members**: There are 25 members participating, and they can either pick up litter (p) or clean hallways (c). Thus, the first equation is:
\[
p + c = 25
\]
2. **Total Funds Raised**: The council wants to raise $300, with members earning $15 for each member that picks up litter and $10 for each member that cleans hallways. Therefore, the second equation is:
\[
15p + 10c = 300
\]
Thus, the pair of linear equations that model this situation is:
\[
\begin{align*}
1. & \quad p + c = 25 \\
2. & \quad 15p + 10c = 300
\end{align*}
\]
The correct choice from the provided options is:
**p+c=25; 15p+10c=300**.
1. **Total Members**: There are 25 members participating, and they can either pick up litter (p) or clean hallways (c). Thus, the first equation is:
\[
p + c = 25
\]
2. **Total Funds Raised**: The council wants to raise $300, with members earning $15 for each member that picks up litter and $10 for each member that cleans hallways. Therefore, the second equation is:
\[
15p + 10c = 300
\]
Thus, the pair of linear equations that model this situation is:
\[
\begin{align*}
1. & \quad p + c = 25 \\
2. & \quad 15p + 10c = 300
\end{align*}
\]
The correct choice from the provided options is:
**p+c=25; 15p+10c=300**.