Jenny bought five pencils and six pens for a total cost of 928$ Fred bought seven pencils and three pens for a total cost of 716$ what is the cost of each item?

1 Answer
Jul 29, 2018

The cost of each pencil is $56.
The cost of each pen is $108.
Those are expensive pencils and pens!

Explanation:

Translate the expression into a system of equations:

color(red)(a) = cost of pencils
color(blue)(b) = cost of pens

5 color(red)(pencils) and 6 color(blue)(pens) for a total of $928.
7 color(red)(pencils) and 3 color(blue)(pens) for a total of $716.

{(5color(red)(a)+6color(blue)(b)=928),(7color(red)(a)+3color(blue)(b)=716):}

To solve, we can use elimination. In this case, it'll be easy to remove the color(blue)(b) term, so we multiply the bottom equation by two:

{(5color(red)(a)+6color(blue)(b)=928),(14color(red)(a)+6color(blue)(b)=1432):}

And then we subtract the upper equation from it:

9color(red)(a)=504
color(red)(a)=56

We can plug color(red)(a) back into one of the original equations to get color(blue)(b).

5(56)+6color(blue)(b)=928
280+6color(blue)(b)=928
6color(blue)(b)=648
color(blue)(b)=108

We have color(red)(a)=56 and color(blue)(b)=108.
This means color(red)(pencils) cost $56 and color(blue)(pens) cost $108.