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?

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Answer 1 · 2018-07-29T00:06:36

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

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#.