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2013 AMC 10A Problem 10

Problem 10 of 25EasierArithmetic

A flower bouquet contains pink roses, red roses, pink carnations, and red carnations. One third of the pink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations?

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Solution

Let the total number of flowers be x.x. There are 0.6x0.6x pink flowers and 0.4x0.4x red flowers. Then there are 13⋅0.6x=0.2x \dfrac{1}{3} \cdot 0.6x = 0.2x pink roses, which means there are 0.4x0.4x pink carnations. There are also 34⋅0.4x=0.3x \dfrac{3}{4} \cdot 0.4x = 0.3x red carnations. This means there are 0.3x+0.4x=0.7x0.3x + 0.4x = 0.7x carnations. This is 70%70\% of the total flowers. Thus, E is the correct answer.
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