At the Henderson Middle School awards ceremony, the principal is going to honor outstanding students with gift cards. The gift cards for excellent grades, g

Question

, are worth $40, and the gift cards for perfect attendance, a
, are worth $25. The principal has $4,000 allotted for this event, and he is going to recognize 100 students. Write the pair of linear equations that model this situation.(1 point)
Equation to represent the total number of students:
= 100
Equation to represent the total cost of the gift cards:
= 4,000
Remaining Attempts : 3

Answer 1

To model the situation with linear equations, we can define two variables:

• Let \( g \) represent the number of students receiving gift cards for excellent grades.
• Let \( a \) represent the number of students receiving gift cards for perfect attendance.

We know the following from the problem:

1. The total number of students is 100.
2. The total cost of the gift cards is $4,000.

Based on this information, we can write the following equations:

1. For the total number of students: \[ g + a = 100 \]

2. For the total cost of the gift cards: \[ 40g + 25a = 4000 \]

Thus, the pair of linear equations that model this situation is: \[ \begin{align*}

1. & \quad g + a = 100 \
2. & \quad 40g + 25a = 4000 \end{align*} \]