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Algebra Difficulty 3.9 AMC 10/12 Find the answer North Macedonia

Maja went to the bookstore to buy two books. The price of the first book was 65%65\% and the price of the other 57.5%57.5\% from the money that Maja had with her. She needed additional 4545 denars to buy the two books. How much money did Maja have with her?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Let Maja had xx denars with her. Then from the condition in the problem we have that
65100x+57.5100x=45+x. \frac{65}{100}x + \frac{57.5}{100}x = 45 + x.
So we obtain that
65x+57.5x=4500+100x. 65x + 57.5x = 4500 + 100x.
122.5x=4500+100x 122.5x = 4500 + 100x
22.5x=4500 22.5x = 4500
x=200. x = 200.
So Maja had 200200 denars with her.

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