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
Equation to represent the total number of students: g + a = 100
Equation to represent the total cost of the gift cards: 40g + 25a = 4000
To write the pair of linear equations that model the situation, let's assign variables to the unknown quantities in the problem.
Let the number of gift cards for excellent grades be represented by the variable g.
Let the number of gift cards for perfect attendance be represented by the variable a.
1. Equation to represent the total number of students:
Since the principal is going to recognize 100 students, the equation would be:
g + a = 100
2. Equation to represent the total cost of the gift cards:
The gift cards for excellent grades, g, are worth $40 each, so the total value of those gift cards is 40g.
The gift cards for perfect attendance, a, are worth $25 each, so the total value of those gift cards is 25a.
As the principal has $4,000 allotted, the equation would be:
40g + 25a = 4000
Therefore, the pair of linear equations that model this situation would be:
1. g + a = 100
2. 40g + 25a = 4000