Question

Sam wants to buy 8 pencils and 6 pens, which cost a total of $8.50. He realizes he doesn't have enough cash and instead takes only 4 of each, which costs only $5. What is the price of each pen and pencil? pen, $0.75; pencil, $0.50

Answer 1

x = pencils, y = pens

8x + 6y = 8.50
4x + 4y = 5.....multiply by -2
----------------
8x + 6y = 8.50
-8x - 8y = -10 (result of multiplying by -2)
-----------------add
-2y = - 1.50
y = -1.50 / -2
y = 0.75 <=== pens cost 0.75

4x + 4y = 5
4x + 4(0.75) = 5
4x + 3 = 5
4x = 5 - 3
4x = 2
x = 2/4
x = 0.50 <== pencils cost 0.50