At the Henderson Middle school awards ceremony, the principal is going to honor outstanding student with gift cards. The gift cards for excellent grades, g, are worth $40 and the gift card 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.
Let's represent the number of students receiving the gift cards for excellent grades as g and the number of students receiving the gift cards for perfect attendance as a.
The value of the gift cards for excellent grades is $40, meaning that the total value of the gift cards for excellent grades is 40g.
The value of the gift cards for perfect attendance is $25, meaning that the total value of the gift cards for perfect attendance is 25a.
The total number of students receiving gift cards is 100, so we have the equation g + a = 100.
The total budget for the event is $4,000, so we have the equation 40g + 25a = 4000.
Therefore, the pair of linear equations that model this situation are:
g + a = 100
40g + 25a = 4000
Let's assume the number of students receiving gift cards for excellent grades is represented by variable x, and the number of students receiving gift cards for perfect attendance is represented by variable y.
The value of the gift cards for excellent grades (g) is $40, and the value of the gift cards for perfect attendance (a) is $25.
From the given information, we know the total money allotted is $4,000, and the total number of students being recognized is 100.
The first equation can be derived from the total cost of gift cards for excellent grades:
40x
The second equation can be derived from the total cost of gift cards for perfect attendance:
25y
Since the total money allotted for the event is $4,000, the sum of the costs of both types of gift cards must equal that amount:
40x + 25y = 4000
Since the principal wants to recognize 100 students, the total number of students receiving gift cards must be 100:
x + y = 100
The pair of linear equations representing this situation are:
40x + 25y = 4000
x + y = 100
To write the pair of linear equations that model this situation, we need to consider the number of gift cards for excellent grades (g) and the number of gift cards for perfect attendance (a).
First, let's define our variables:
Let g represent the number of gift cards for excellent grades.
Let a represent the number of gift cards for perfect attendance.
Now, let's convert the given information into equations:
1. The value of the gift cards for excellent grades (g) multiplied by $40 should be equal to the total amount allotted for the event:
40g = Total amount allotted
2. The value of the gift cards for perfect attendance (a) multiplied by $25 should also be equal to the total amount allotted for the event:
25a = Total amount allotted
3. Additionally, since the principal is going to recognize a total of 100 students, the sum of the number of gift cards for excellent grades (g) and the number of gift cards for perfect attendance (a) should equal 100:
g + a = 100
So, the pair of linear equations that model this situation are:
40g = Total amount allotted
25a = Total amount allotted
g + a = 100