If you buy 2 pens and 3 pencils, you get $4 change from a $10 bill. If you buy 4 pens and 2 pencils, the cost is $8. Find the cost of one pen expressed in terms of dollars.

Question

I’m having a hard time setting up the problem.

Answer 1

Let n = the # of pens. Let c = the number of pencils.

2n + 3c = 6

4n + 2c = 8

Let's multiply the top by -2 to make the x's opposites.

-4n - 6c = -12

4n + 2c = 8

Adding them together...

-4c = -4

c = 1

2n + 3(1) = 6

2n + 3 = 6

2n = 3

n = 1.5

$1.50