Question

Question 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 , 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

Answer 1

To model the situation, we can define two variables:

Let \( g \) be the number of gift cards given for excellent grades (worth $40 each), and let \( a \) be the number of gift cards given for perfect attendance (worth $25 each).

Based on the information given, we can write the following pair of linear equations:

1. For the total number of students recognized, we have:

\[
g + a = 100
\]

2. For the total cost of the gift cards, we have:

\[
40g + 25a = 4000
\]

Thus, the pair of linear equations that model this situation is:

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