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 pen, $0.50; pencil, $0.25 pen, $1.00; pencil, $0.25 pen, $0.80; pencil, $0.35 pen, $1.20; pencil, $0.25

Answer 1

4l+4i=5 (l=lead, i=ink :P)

4l=5-4i

l=(5-4i)/4

l=1.25-i

...

8l+6i=8.5, using l found above in this gives you:

8(1.25-i)+6i=8.5 perform indicated multiplication on left side

10-8i+6i=8.5 combine like terms on left side

10-2i=8.5 subtract 10 from both sides

-2i=-1.5 divide both sides by -2

i=0.75, since l=1.25-i

l=0.50

So the cost of a pen is $0.75 and the cost of a pencil is $0.50