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
Let's call the number of students receiving excellent grades as x and the number of students with perfect attendance as y.
Equation to represent the total number of students:
x + y = 100
Equation to represent the total cost of the gift cards:
40x + 25y = 4,000
Equation to represent the total number of students:
g + a = 100
Equation to represent the total cost of the gift cards:
40g + 25a = 4,000
To write the pair of linear equations that model this situation, let's use the variables "g" and "a" to represent the number of gift cards for excellent grades and perfect attendance, respectively.
Equation to represent the total number of students:
Since the principal is going to recognize a total of 100 students, we can write the equation:
g + a = 100
Equation to represent the total cost of the gift cards:
Since each gift card for excellent grades is worth $40 and each gift card for perfect attendance is worth $25, we can write the equation to represent the total cost of the gift cards:
40g + 25a = 4000