Question

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?

$15$

$30$

$40$

$60$

$70$

Solution:

Six tenths of the flowers are pink and four tenths are red. Since two thirds of the pink flowers are carnations, pink carnations make up $\tfrac{2}{3}\cdot\tfrac{6}{10} = \tfrac{4}{10}$ of the flowers.

Since three fourths of the red flowers are carnations, red carnations make up $\tfrac{3}{4}\cdot\tfrac{4}{10} = \tfrac{3}{10}$ of the flowers. Together the carnations are $\tfrac{4}{10} + \tfrac{3}{10} = \tfrac{7}{10} = 70\%.$

Thus, the correct answer is E.

2013 AMC 12A Problem 3

Solution:

Problem 3 in Other Years