Real-World Systems of Equations Practice

Question

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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.(1 point)
Equation to represent the total number of students:
= 100
Equation to represent the total cost of the gift cards:
= 4,000

Answer 1

To model the situation with a pair of linear equations, we can use two variables:

Let:

• \( g \) = the number of gift cards for excellent grades.
• \( a \) = the number of gift cards for perfect attendance.

From the information provided, we can form the following equations:

1. Equation to represent the total number of students: \[ g + a = 100 \]

2. Equation to represent the total cost of the gift cards: \[ 40g + 25a = 4000 \]

So, the pair of linear equations that model this situation is:

1. \( g + a = 100 \)
2. \( 40g + 25a = 4000 \)