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

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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) About Me  (Show Source):
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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.