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
Equation to represent the total number of students:
g + a = 100
Equation to represent the total cost of the gift cards:
40g + 25a = 4000
Let's let "x" represent the number of students who receive gift cards for excellent grades and "y" represent the number of students who receive gift cards for perfect attendance.
The first equation that represents the total number of students is:
x + y = 100
The second equation that represents the total cost of the gift cards is:
40x + 25y = 4,000
To write the pair of linear equations that model this situation, we need to define two variables and express them in terms of the given information.
Let's define:
- g as the number of gift cards for excellent grades
- a as the number of gift cards for perfect attendance
Equation to represent the total number of students:
Since the total number of students who will receive gift cards is 100:
g + a = 100
Equation to represent the total cost of the gift cards:
Given that the gift cards for excellent grades (g) are worth $40 each, and the gift cards for perfect attendance (a) are worth $25 each, we can calculate the total cost:
40g + 25a = 4000
Therefore, the pair of linear equations that model this situation are:
g + a = 100
40g + 25a = 4000