At the Henderson middle school awards ceremony the principal is going to honor outstanding students with gift cards. The gift cards for excellence grades g are worth $40 and the gift cards for perfect attendance a are worth $25. The principal has $4000 allotted for this event and he is going to recognize 100 students. Write the pair of linear equations that model this situation.
Let's assume x represents the number of students with excellence grades and y represents the number of students with perfect attendance.
The first equation would represent the total number of students being recognized:
x + y = 100
The second equation would represent the total amount of money the principal has allotted for gift cards:
40x + 25y = 4000
Therefore, the pair of linear equations would be:
x + y = 100
40x + 25y = 4000