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.

Answer 1

Let's say the number of students receiving gift cards for excellent grades is represented by the variable 'x' and the number of students receiving gift cards for perfect attendance is represented by the variable 'y'.

The first equation will represent the value of gift cards for excellent grades:

40x

The second equation will represent the value of gift cards for perfect attendance:

25y

Since the number of students receiving gift cards is 100, the sum of 'x' and 'y' should equal 100:

x + y = 100

To find the total value of the gift cards, we can add the equations:

40x + 25y = 4000

So, the pair of linear equations that models this situation are:

x + y = 100
40x + 25y = 4000