Question

Julio bought 4 pencils and 3 erasers for $0.37 and David paid $0.33 for 3 pencils and 4 erasers. What is the cost of one pencil? What is the cost of one eraser?

Answer 1

Each pencil costs $0.07 and each eraser costs $0.03

Explanation:

System of linear equations

It refers to the study of systems when n variables are related in m linear equations, each one is not independent from the others. Solving such systems can be done following very diverse approaches.

Let p=the price of each pencil while e is the price each eraser

Julio bought 4 pencils and 3 erasers, spending

`4p+3e=0.37`

David bought 3 pencils and 4 erasers, spending

`3p+4e=0.33`

The system of equations is written in the form

`\left\{\begin{matrix}4p+3e=0.37\\ 3p+4e=0.33\end{matrix}\right`

We'll solve it by reduction. Multiplying the first equation by -3 and the second by 4:

`\left\{\begin{matrix}-12p-9e=-1.11\\ 12p+16e=1.32\end{matrix}\right.`

Adding both equations:

7e=0.21

e=0.03

Multiplying the first one by -4 and the second by 3

`\left\{\begin{matrix}-16p-12e=-1.48\\ 9p+12e=0.99\end{matrix}\right.\end{matrix}\right.`

Adding both equations:

-7p=-0.49

p=0.07

Solution: Each pencil costs $0.07 and each eraser costs $0.03