SOLUTION: At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five

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Question 104979This question is from textbook University of Phoenix Elementary and Intermediate Algebra
: At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?
So first of all, I think all of the tutors are awesome!!! Thank you so much for offfering your services. My question on this is I need to write a system of 2 equations in 2 unknowns and then solve it. How would I set this up?This question is from textbook University of Phoenix Elementary and Intermediate Algebra

Answer by elima(1433) (Show Source):
You can put this solution on YOUR website!
At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $1.45, and June bought two books and five magazines for $1.25. What was the price of a book and what was the price of a magazine?
Harriet bought = 4B, 3M
June bought = 2B, 5M
Now lets set them as equations, we know the total amount each spent, so we just make what they bought equal to those;
Harriet;
4B+3M=1.45
June;
2B+5M=1.25
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Now we will go ahead and solve using the elimination method;
4B+3M=1.45
2B+5M=1.25
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I will multiply the second equation by -2 so I can eliminate the B;
4B+3M=1.45
-4B-10M=-2.5
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Now add equations together;
-7M=-1.05
divide each side by -7;
M=.15
Now plug that answer into either equation for M;
4B+3(.15)=1.45
4B+.45=1.45
4B=1.00
B=.25
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so our Books = .25
Magazines = .15
:)