Question
The Lincoln High School Student Council wants to raise $300 to make a donation to a homeless shelter. To help 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 hallway, c. All 25 members of the student council will be participating. Write the pair of linear equations that model this situation
Answers
GPT-4o mini
To model the situation with a pair of linear equations, we can define the following variables:
- \( p \): the number of student council members who pick up litter outside.
- \( c \): the number of student council members who clean the hallway.
We know the following from the problem:
1. There are a total of 25 members in the student council:
\[
p + c = 25
\]
2. The goal is to raise $300 through their efforts, with each member picking up litter earning $15 and each member cleaning the hallway earning $10:
\[
15p + 10c = 300
\]
Combining these, we can write the pair of linear equations that model this situation:
1. \( p + c = 25 \) (Total number of members)
2. \( 15p + 10c = 300 \) (Total amount of money to be raised)
These two equations represent the conditions given in the problem for the Student Council's fundraising efforts.
- \( p \): the number of student council members who pick up litter outside.
- \( c \): the number of student council members who clean the hallway.
We know the following from the problem:
1. There are a total of 25 members in the student council:
\[
p + c = 25
\]
2. The goal is to raise $300 through their efforts, with each member picking up litter earning $15 and each member cleaning the hallway earning $10:
\[
15p + 10c = 300
\]
Combining these, we can write the pair of linear equations that model this situation:
1. \( p + c = 25 \) (Total number of members)
2. \( 15p + 10c = 300 \) (Total amount of money to be raised)
These two equations represent the conditions given in the problem for the Student Council's fundraising efforts.