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Question 8785: I am helping my daughter with her homework and need HELP, Please. The question is.....In a stationery store, pencils have one price and pens have another. Two pencils and three pens cost 78 cents. But three pencils and two pens cost 72 cents. How much does one pencil cost?
Thanks.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! First you'll need to set up your equations from the information in the problem description. You'll need two variables, one to represent the number of pens and the other to represent the number of pencils.
You could use P for pens and W for (wooden) pencils.
From the description, you can now write two equations.
2W + 3P = $0.78 and
3W + 2P = $0.72
Now you need to solve this system of equations. One way is to use the "elimination" method. In this method, you would multiply one or both equations by the appropriate integers so as to make both equations have the same number of one of the two variables. This sounds more complicated than it really is. Take a look below:
2(2W + 3P = $0/78) = 4W + 6P = $1.56
3(3W + 2P = $0.72) = 9W + 6P = $2.16
Now, you subtract the first new equation from the second new equation and when you do this, you eliminate the variable P, leaving you with just one variable (W), the number of pencils.
After the subtraction, you get:
5W = $0.60 Now divide both sides of the equation by 5 to get W.
W = $0.12
So, one pencil costs $0.12 or 12 cents.
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