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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.

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To form the pair of linear equations that model this situation, we can define two variables:

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

Based on the information provided:

  1. Each gift card for excellent grades is worth $40, and each gift card for perfect attendance is worth $25. The total amount of money allotted for the gift cards is $4,000. This gives us the first equation based on the total cost:

\[ 40g + 25a = 4000 \]

  1. The principal is recognizing a total of 100 students, which gives us the second equation based on the total number of awards:

\[ g + a = 100 \]

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

\[ \begin{aligned}

  1. & \quad 40g + 25a = 4000 \
  2. & \quad g + a = 100 \end{aligned} \]