Using a system of equations, it is found that:
- Each individual notebook costs $2.75.
- A package of pencils costs $1.25.
- Each individual marker costs $0.5.
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:
- n is the price of a notebook.
- p is the price of a package of pencils.
- m is the price of marker.
From Stan's purchases, we have that:
[tex]n + 3p + 2m = 7.5[/tex]
From Jan's purchases, we have that:
[tex]2n + 6p + 5m = 15.50[/tex]
From Fran's purchases, we have that:
[tex]n + 2p + 2m = 6.25[/tex]
From the third equation:
[tex]n = 6.25 - 2p - 2m[/tex]
Replacing on the first:
[tex]n + 3p + 2m = 7.5[/tex]
[tex]6.25 - 2p - 2m + 3p + 2m = 7.5[/tex]
[tex]p = 1.25[/tex]
On the second equation, we have that:
[tex]2n + 6p + 5m = 15.50[/tex]
[tex]2(6.25 - 2p - 2m) + 6(1.25) + 5m = 15.50[/tex]
[tex]2(3.75 - 2m) + 5m = 8[/tex]
[tex]m = 0.5[/tex]
Finally:
[tex]n = 6.25 - 2(1.25) - 2(0.5) = 2.75[/tex]
Then:
- Each individual notebook costs $2.75.
- A package of pencils costs $1.25.
- Each individual marker costs $0.5.
To learn more about system of equations, you can take a look at https://brainly.com/question/24342899
