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?
Let x be the book price and y be the magazine price, both in cents. Your statements about the two purchases can be written
4x + 3y = 145
and
2x + 5y = 125
Now solve those two equations for x and y. A good first step would be to convert (double both sides of) the second equation to give you
4x + 10 y = 250
Combining that with the first equation can eliminate the x variable and give you
7 y = 105
y = 15 cents
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