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.

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.
Equation to represent the total number of students:  = 100 Equation to represent the total cost of the gift cards: = 4,000

GPT 3.5 · Answer

Let g represent the number of gift cards for excellent grades and a represent the number of gift cards for perfect attendance.

The equation to represent the total number of students is:

g + a = 100

The equation to represent the total cost of the gift cards is:

40g + 25a = 4000