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 $4000 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:
Equation to represent the total cost of gift cards:
Let's assume x is the number of students who receive gift cards for excellent grades (g) and y is the number of students who receive gift cards for perfect attendance (a).
Equation to represent the total number of students:
x + y = 100
Equation to represent the total cost of gift cards:
40x + 25y = 4000
that’s wrong?
Apologies for the mistake. Let's correct the equations.
Let's assume x is the number of students who receive gift cards for excellent grades (g) and y is the number of students who receive gift cards for perfect attendance (a).
Equation to represent the total number of students:
x + y = 100
Equation to represent the total cost of gift cards:
40x + 25y = 4000
To write the pair of linear equations that model this situation, we need to consider the two variables, g and a.
1. Equation to represent the total number of students:
Since the total number of students to be recognized is 100, we can represent this equation as:
g + a = 100
2. Equation to represent the total cost of gift cards:
The principal has $4000 allotted for the event, so we can represent this equation as:
40g + 25a = 4000
These two equations can help us determine the values of g and a in order to meet the requirements of recognizing 100 students and staying within the budget of $4000.