Question

Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil. What would one pencil and one pen cost?

Answer 1

$12x+20y=16$ where x is a pen and y is a pencil. Because a pen is .40 more than a pencil we can write this in terms of pencils and extra .40:

$32y+12*.4 = 16\\=32y+4.8 = 16\\=32y+4.8-4.8 = 16-4.8\\=32y = 11.2\\=32y/32 = 11.2/32\\=y = 0.35$

Therefore, a pencil costs 0.35 and a pen costs 0.75. Combined, one of each costs 1.10 dollars.