Amy purchased 17 pencils and 18 pens for a fund-raiser at school and spent $61.50. Jocelyn purchased 10 pencils and 21 pens and spent $57. How much does each pencil cost?

Answer 1

X is price of the pencil

Y is price of the pen.

The amounts are in pennies

17X + 18Y = 6150

10X + 21Y = 5700

Solves by elimination: Multiplies top equation by 10 and bottom equation by 17

170x + 180y = 61500

170x + 357y = 96900

Subtracts BOTTOM MINUS TOP

177y = 35400

y = 200

then x = (5700 - 21*200)/10 per original bottom equation

= (5700 - 4200)/10

= 1500/10

= 150

So the pencil costs $1.50 and the pen costs $2.00