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's represent the number of students who receive gift cards for excellent grades as x, and the number of students who receive gift cards for perfect attendance as y.

The total number of students recognized is 100:
x + y = 100

The total cost of the gift cards is $4,000:
40x + 25y = 4000

Answer 2

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

Let's use the variables "g" and "a" to represent the number of students receiving gift cards for excellent grades and perfect attendance, respectively.

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

Therefore, the pair of linear equations that model this situation is:
g + a = 100
40g + 25a = 4000

Answer 3

[AI-generated answer — Explain Bot]

To write the pair of linear equations that models this situation, we need to define two variables:

1. The number of students receiving gift cards for excellent grades (g).
2. The number of students receiving gift cards for perfect attendance (a).

First, we need to set up an equation that represents the total number of students being recognized:

Equation 1: g + a = 100

Since the total number of students recognized is 100, we add the number of students receiving gift cards for excellent grades (g) and the number of students receiving gift cards for perfect attendance (a) to get the sum of 100.

Next, we need to set up an equation that represents the total cost of the gift cards:

Equation 2: 40g + 25a = 4000

Since the gift cards for excellent grades (g) are worth $40 and the gift cards for perfect attendance (a) are worth $25, we multiply the number of students receiving each type of gift card by their corresponding value. The sum of these two products should be equal to the total cost of $4,000.

Therefore, the pair of linear equations that models this situation is:

Equation 1: g + a = 100
Equation 2: 40g + 25a = 4000