Difference between revisions of "2013 AMC 12A Problems/Problem 3"

(Created page with "We are given that 6/10, or 3/5 of the flowers are pink, so we know 2/5 of the flowers are red. Since 1/3 of the pink flowers are roses, 2/3 of the pink flowers are carnations. ...")
 
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We are given that 6/10, or 3/5 of the flowers are pink, so we know 2/5 of the flowers are red.
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We are given that <math>\frac{6}{10} = \frac{3}{5}</math> of the flowers are pink, so we know <math>\frac{2}{5}</math> of the flowers are red.
  
Since 1/3 of the pink flowers are roses, 2/3 of the pink flowers are carnations.
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Since <math>\frac{1}{3}</math> of the pink flowers are roses, <math>\frac{2}{3}</math> of the pink flowers are carnations.
  
We are given that 3/4 of the red flowers are carnations.
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We are given that <math>\frac{3}{4}</math> of the red flowers are carnations.
  
 
The number of carnations are  
 
The number of carnations are  
  
(3/5 pink flowers)(2/3 carnations) + (2/5 red flowers)(3/4 carnations) = 2/5 + 3/10 = 7/10 = 70%, or E
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<math>\frac{3}{5} * \frac{2}{3} + \frac{2}{5} * \frac{3}{4} = \frac{2}{5} + \frac{3}{10} = \frac{7}{10} = 10\%</math>

Revision as of 04:24, 7 February 2013

We are given that $\frac{6}{10} = \frac{3}{5}$ of the flowers are pink, so we know $\frac{2}{5}$ of the flowers are red.

Since $\frac{1}{3}$ of the pink flowers are roses, $\frac{2}{3}$ of the pink flowers are carnations.

We are given that $\frac{3}{4}$ of the red flowers are carnations.

The number of carnations are

$\frac{3}{5} * \frac{2}{3} + \frac{2}{5} * \frac{3}{4} = \frac{2}{5} + \frac{3}{10} = \frac{7}{10} = 10\%$

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