SOLUTION: If 10 pens and 15 markers cost $26, and 5 of the same pens and 10 of the same markers cost $16, find the cost of a pen.

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Question 107541: If 10 pens and 15 markers cost $26, and 5 of the same pens and 10 of the same markers cost $16, find the cost of a pen.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
This is a 2 linear equations in 2 variables problem. Let p be the cost of a pen and m be the cost of a marker.

Eq 1) 10p%2B15m=26 and

Eq 2) 5p%2B10m=16

Multiply Eq 2) by -3 and Eq 1) by 2

Eq 3) -15p-30m=-48
Eq 4) 20p%2B30m=52


Then add 3) to 4) term by term:

5p=4
p=0.80


And pens cost 80 cents.

To check the answer, plug the 80 cents into Eq 1 or 2 to determine that markers cost $1.20, then

10%2A0.8%2B15%2A1.20=26 Check.