Question

A pen costs twice as much as a pencil. If 7 pens and 12 pencils cost $6.50, find the cost of a pencil.

I know the answer (pencil $0.25, pen $0.5), but I need to figure out how the answer is solved.

Answer 1

1. Observe the problem

2. Make a system of linear equations

x is pens

y is pencil

As stated in the text, x=2y

x=2y

7x+12y=6.50

Using substitution,

7(2y)+12y=6.50

14y+12y=6.50

26y=6.50

y=0.25

Substituting it back into the first equation:

x=2(0.25)

x=0.5

y=0.25