the gift cards for excellent grades,g, are worth $40, and the gift cards for perfect attendance, a, are worth $25. the principle has $4,00 dollars allotted for this event. and he is going to recognize 100 students. write the pair of linear equations that represents this situation.
Let's assume that the number of gift cards for excellent grades is represented by g and the number of gift cards for perfect attendance is represented by a.
According to the given information, the value of each gift card for excellent grades is $40, and the value of each gift card for perfect attendance is $25.
The total number of gift cards for excellent grades should be equal to the total amount of money allotted for this event, which is $4000.
Therefore, the equation for the number of gift cards for excellent grades can be written as:
40g = 4000
Similarly, the total number of gift cards for perfect attendance should be 100.
Therefore, the equation for the number of gift cards for perfect attendance can be written as:
a = 100
So, the pair of linear equations that represents this situation are:
40g = 4000
a = 100
Let's represent the number of gift cards for excellent grades as "g" and the number of gift cards for perfect attendance as "a".
According to the given information:
1) The gift cards for excellent grades, g, are worth $40 each. This means that the total value of the gift cards for excellent grades will be 40g.
2) The gift cards for perfect attendance, a, are worth $25 each. This means that the total value of the gift cards for perfect attendance will be 25a.
The principle has a total of $4,000 allotted for this event. This means that the total value of the gift cards cannot exceed $4,000. So, we can write the first equation as:
40g + 25a = 4000
The principle wants to recognize 100 students in total. This means that the total number of gift cards cannot exceed 100. So, we can write the second equation as:
g + a = 100
Therefore, the pair of linear equations that represents this situation is:
40g + 25a = 4000
g + a = 100
To create the pair of linear equations that represents this situation, we can define the variables x and y as follows:
Let x represent the number of gift cards for excellent grades (g)
Let y represent the number of gift cards for perfect attendance (a)
First, we need to establish the constraints of the problem:
1. The gift cards for excellent grades (g) are worth $40.
2. The gift cards for perfect attendance (a) are worth $25.
3. The principle has $4000 allotted for this event.
4. The principle is going to recognize 100 students.
Based on these constraints, we can create the following pair of linear equations:
Equation 1: x + y = 100
This equation represents the fact that the total number of students recognized should be equal to 100.
Equation 2: 40x + 25y = 4000
This equation represents the fact that the total value of the gift cards for excellent grades (40x) and perfect attendance (25y) should not exceed the total amount allotted, which is $4000.
These two equations together form the pair of linear equations that represent the given situation.