SOLUTION: Solve, using two equations in two variables If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy four pens and two mechan

Question 120175This question is from textbook Algebra Structure and Method
: Solve, using two equations in two variables
If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you'll get $2 change. How much does each pen and each pencil cost?

If anyone can answer this problem I would deeply appreciate it. Please and Thank You!!!! This question is from textbook Algebra Structure and Method

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you'll get $2 change. How much does each pen and each pencil cost?
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Let "p" be the price of a pen; Let "m" be the price of a pencil.
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EQUATIONS:
6p + m = 9
4p + 2m=8
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Multiply thru 1st equation by 2 to get:
12p + 2m = 18
Subtract from the 2nd equation:
-8p = -10
p = 10/8 = $1.25 (price of a pen)
Substitute to find "m":
6(1.25)+m = 9
7.50 + m = 9
m = $1.50 (price of a michanical pencil)
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Cheers,
Stan H.

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