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?

Answer 1

Pens are 75 cents, and pencils are 50 cents

Answer 2

8p+6i=8.5
4p+4i=5
4p=5-4i
p=1.25-i
8(1.25-i)+6i=8.5
10-8i+6i=8.5
10-2i=8.5
-2i=-1.5
i=.75
4p+4(.75)=5
4p+3=5
4p=2
p=.5

Answer 3

Let the price of one pencil and one pen be x and y dollars respectively.
Therefore from first condition, we have:
8x +6 y = 8.5--------(1)
Now from second condition, we have:
4x + 4y = 5--------(2)
Multiplying eq 2 by 2 and then subtracting it from (1), we get.
8x +6 y -(8x + 8y) = 8.5- 10
8x +6 y -8x - 8y = -1.5
-2y = -1.5
y= -1.5/-2= 1.5/2= 0.75
from eq (2) we get
4x + 4*0.75 = 5
4x + 3 = 5
4x = 5-3
4x = 2
x= 2/4= 0.5
Thus the price of each pencil and pen is $0.5 and $0.75 respectively.