Respuesta :
Using a system of equations, it is found that:
- Each pen costs $0.6.
- Each folder costs $0.4.
- Each notebook costs $4.4.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
- Variable x: The cost of a pen.
- Variable y: The cost of a folder.
- Variable z: The cost of a notebook
John bought 2 pens, 3 folders, and 4 notebooks for a total of $20, hence:
2x + 3y + 4z = 20.
Cindy bought 5 folders and 5 notebooks for a total of $25, hence:
5y + 5z = 25.
x + z = 5.
x = 5 - z.
Isaiah bought 3 pens, 1 folder, and 2 notebooks for a total of $11, hence:
3x + y + 2z = 11.
y = 11 - 3x - 2z
Replacing the second and the third equation on the first, we have that:
2x + 3y + 4z = 20.
2(5 - z) + 3(11 - 3x - 2z) + 4z = 20.
10 - 2z + 3[11 - 3(5 - z) - 2z] + 4z = 20.
2z + 3(11 - 15 + 3z - 2z) = 10
2z + 3(z - 4) = 10
5z = 22.
z = 4.4
x = 5 - z = 5 - 4.4 = 0.6
y = 11 - 3x - 2z = 11 - 3(0.6) - 2(4.4) = 0.4.
Hence:
- Each pen costs $0.6.
- Each folder costs $0.4.
- Each notebook costs $4.4.
More can be learned about a system of equations at https://brainly.com/question/24342899
