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 __= 4000
Equation to represent the total number of students: g + a = 100
Equation to represent the total cost of the gift cards 40g + 25a = 4000
Equation to represent the total number of students: x + y = 100
Equation to represent the total cost of the gift cards: 40x + 25y = 4000
In these equations, x represents the number of students receiving excellent grades gift cards, and y represents the number of students receiving perfect attendance gift cards.
To solve this problem, we need to set up two linear equations.
1. Equation to represent the total number of students:
The total number of students to be recognized is 100. We can represent this with the variable "s" (for students). Since we have only one variable involved, the equation is simply:
s = 100
2. Equation to represent the total cost of the gift cards:
The principal has $4,000 allotted for this event. We need to find the total cost of the gift cards based on the number of students receiving gift cards. Let's represent the number of students receiving gift cards for excellent grades as "g" and the number of students receiving gift cards for perfect attendance as "a".
The value of each gift card for excellent grades is $40, so the total cost of the gift cards for excellent grades is 40g.
The value of each gift card for perfect attendance is $25, so the total cost of the gift cards for perfect attendance is 25a.
The total cost of the gift cards should equal $4,000, so the equation is:
40g + 25a = 4000