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.
Let's define our variables:
g = number of gift cards for excellent grades
a = number of gift cards for perfect attendance
Given information:
The value of each gift card for excellent grades (g) is $40.
The value of each gift card for perfect attendance (a) is $25.
The principal has $4,000 allotted for this event.
He is going to recognize 100 students.
Now let's write the equations:
1. The equation for the total value of gift cards for excellent grades:
40g
2. The equation for the total value of gift cards for perfect attendance:
25a
3. The equation for the total number of gift cards:
g + a = 100
4. The equation for the total cost of all the gift cards:
40g + 25a = 4000
So the pair of linear equations that model this situation are:
Equation 1: g + a = 100
Equation 2: 40g + 25a = 4000
To write the pair of linear equations that model this situation, we need to define two variables: g (representing the number of gift cards for excellent grades) and a (representing the number of gift cards for perfect attendance).
Since the principal is going to recognize 100 students, we know that the total number of gift cards given will be equal to 100:
g + a = 100
Since the gift cards for excellent grades are worth $40 and the gift cards for perfect attendance are worth $25, the total value of all the gift cards given should be $4,000:
40g + 25a = 4000
Therefore, the pair of linear equations that model this situation are:
g + a = 100
40g + 25a = 4000
Let's say the number of students receiving gift cards for excellent grades is represented by the variable 'x' and the number of students receiving gift cards for perfect attendance is represented by the variable 'y'.
The first equation will represent the value of gift cards for excellent grades:
40x
The second equation will represent the value of gift cards for perfect attendance:
25y
Since the number of students receiving gift cards is 100, the sum of 'x' and 'y' should equal 100:
x + y = 100
To find the total value of the gift cards, we can add the equations:
40x + 25y = 4000
So, the pair of linear equations that models this situation are:
x + y = 100
40x + 25y = 4000