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

Question

𝑝
, and $10 for each member who cleans the hallways, c
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
𝑝
+
𝑐
=
300
; 15p+10c=25
15
𝑝
+
10
𝑐
=
25
p plus c equals 300 ; 15 p plus 10 c equals 25

p+c=25
𝑝
+
𝑐
=
25
; 15p+10c=300
15
𝑝
+
10
𝑐
=
300
p plus c equals 25 ; 15 p plus 10 c equals 300

p+c=300
𝑝
+
𝑐
=
300
; 10p+15c=25
10
𝑝
+
15
𝑐
=
25
p plus c equals 300 ; 10 p plus 15 c equals 25

p+c=25
𝑝
+
𝑐
=
25
; 10p+15c=300

Answer 1

To model the situation described, we need to create two equations based on the conditions given.

1. Total number of council members: Since all 25 members of the student council will be participating, we have: \[ p + c = 25 \] where \( p \) is the number of members picking up litter, and \( c \) is the number of members cleaning the hallways.

2. Total amount of money raised: The students want to raise $300, with each member that picks up litter earning $15 and each that cleans the hallways earning $10. Thus, we can write: \[ 15p + 10c = 300 \]

The correct pair of linear equations that model this situation is:

\[ \begin{align*}

1. & \quad p + c = 25 \
2. & \quad 15p + 10c = 300 \end{align*} \]

Among the options you provided, this combination corresponds to:

p + c = 25; 15p + 10c = 300