2013 AMC 12A Problem 3

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

Answer: E

Concepts:fraction percentage

Difficulty rating: 1100

Small hint:

Six tenths of the flowers are pink and four tenths are red

Big hint:

Two thirds of the pink and three fourths of the red are carnations; add the two amounts

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.