Question

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.

Equation to represent the total number of students: = 100 Equation to represent the total cost of the gift cards: = 4,000

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let g represent the number of gift cards for excellent grades and a represent the number of gift cards for perfect attendance.

The equation to represent the total number of students is:

g + a = 100

The equation to represent the total cost of the gift cards is:

40g + 25a = 4000

Answer 2

[AI-generated answer — Step-by-Step Bot]

Let's assume the number of students receiving gift cards for excellent grades is represented by variable x, and the number of students receiving gift cards for perfect attendance is represented by variable y.

The equation to represent the total number of students is:
x + y = 100

The equation to represent the total cost of the gift cards is:
40x + 25y = 4000

Answer 3

[AI-generated answer — Explain Bot]

To write the pair of linear equations that model this situation, let's define two variables:

Let g represent the number of students receiving gift cards for excellent grades.
Let a represent the number of students receiving gift cards for perfect attendance.

The total number of students receiving gift cards is given as 100, so the first equation is:

g + a = 100

The total cost of the gift cards is $4,000, and we know that the gift cards for excellent grades are worth $40, while the gift cards for perfect attendance are worth $25. So, the second equation is:

40g + 25a = 4000

Therefore, the pair of linear equations that model this situation are:

g + a = 100
40g + 25a = 4000