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 $40 and the gift cards for perfect attendance a are worth $25 the principal has $4000 allotted for this event and he is going to recognize 100 students. Write the pair of linear equations that model this situation
Let's represent the number of students who receive gift cards for excellent grades as "g" and the number of students who receive gift cards for perfect attendance as "a". We can create two linear equations based on the given information.
First equation:
The total number of gift cards for excellent grades (g) multiplied by $40 should equal the total amount spent on gift cards for excellent grades.
40g = total amount spent on gift cards for excellent grades
Second equation:
The total number of gift cards for perfect attendance (a) multiplied by $25 should equal the total amount spent on gift cards for perfect attendance.
25a = total amount spent on gift cards for perfect attendance
We also know that the total number of students recognized is 100:
g + a = 100
Therefore, the pair of linear equations that model this situation are:
40g + 25a = 4000
g + a = 100
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 given information can be translated into two linear equations:
1. The total amount spent on gift cards for excellent grades (g) is $40 per gift card:
40g
2. The total amount spent on gift cards for perfect attendance (a) is $25 per gift card:
25a
The total amount spent on gift cards should equal the allotted budget of $4000:
40g + 25a = 4000
Furthermore, we know that the number of students receiving gift cards should add up to 100:
g + a = 100
Thus, the pair of linear equations that model this situation are:
40g + 25a = 4000
g + a = 100
To write a pair of linear equations that model this situation, we need to define the variables and assign values based on the given information.
Let's assume:
- Number of gift cards for excellent grades as 'g'
- Number of gift cards for perfect attendance as 'a'
The total value of gift cards for excellent grades can be calculated by multiplying the number of excellent grades cards (g) by $40, so this can be expressed as:
Value of excellent grades cards = $40g
Similarly, the total value of gift cards for perfect attendance can be calculated by multiplying the number of perfect attendance cards (a) by $25, so this can be expressed as:
Value of perfect attendance cards = $25a
The principal has a total budget of $4000, so the sum of the two types of cards cannot exceed this amount. Therefore, we can write the equation:
$40g + $25a ≤ $4000
The principal wants to recognize 100 students in total, so the number of excellent grades cards (g) plus the number of perfect attendance cards (a) should equal 100. We can represent this constraint in the second equation:
g + a = 100
Therefore, the pair of linear equations that model this situation are:
$40g + $25a ≤ $4000
g + a = 100