Question%0D%0AAt the Henderson Middle School awards ceremony, the principal is going to honor outstanding students with gift cards. The gift cards for excellent grades, g%0D%0A%0D%0A, are worth $40, and the gift cards for perfect attendance, a%0D%0A%0D%0A, 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)%0D%0AEquation to represent the total number of students: = 100%0D%0AEquation 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
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
where x represents the number of gift cards for excellent grades and y represents the number of gift cards for perfect attendance.
To write the pair of linear equations that model this situation, we need to define two variables:
Let's denote the number of gift cards for excellent grades as "g".
Let's denote the number of gift cards for perfect attendance as "a".
Now, we can write the equations:
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
The first equation states that the total number of students is the sum of the number of gift cards awarded for excellent grades and the number of gift cards awarded for perfect attendance, which should add up to 100 students.
The second equation represents the total cost of the gift cards. Each gift card for excellent grades is worth $40, so the total cost of the excellent grade gift cards is 40g. Similarly, each gift card for perfect attendance is worth $25, so the total cost of the perfect attendance gift cards is 25a. The sum of these costs should be $4,000, as stated in the question.