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 ma

Question 121454: 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 for a magazine?
Answer by algebrapro18(249) (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 for a magazine?

This problem is solved using a system of linear equations using eliminaiton. First off we need to set up the variables.

x = price of each book
y = price of each magazine

now we set up our system

4x + 3y = 1.45
2x + 5y = 1.25

now we multiply by 100 to clear the decimals

400x + 300y = 145
200x + 500y = 125

Now multiply the second equation by -2.

-400x - 1000y = -250

Now add the first equation to that and cancel the x's and solve for y.

400x + 300y = 145
-400x - 1000y = -250
---------------------
-700y = -105
y = 0.15

now plug that into the first equation and solve for x.

400x + 300(0.15) = 145
400x + 45 = 145
400x = 100
x = 0.25

So each book is priced at 25 cents and each magazine is priced at 15 cents.
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