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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 ninths of the flowers are pink. What percent of the flowers are carnations?

Jan 30, 2021

#1
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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 ninths of the flowers are pink. What percent of the flowers are carnations?

Let's suppose  that we have 36 flowers  (the common denominator of  3,4 and 9)

(6/9)   = (2/3)  of the flowers are pink=  (2/3) (36) = 24

So (1/3)are red  =  12

(2/3)  of the  pink  flowers  are  carnations  =  (2/3) (24) =  16  are pink carnations

Check

(1/3) of the pink flowers are roses = (1/3)  =   8

(3/4)  of the red flowers  are carnations  =  (3/4) (12)   = 9  red carnations

So (1/4)  of the  red flowers are roses = (1/4)(12)   =   3

So  we   have

Pink                                                 Red

Roses     Carnations                   Roses         Carnations

8             16                                3                   9

So    pct  carnations =    (16 + 9)   /36   =  25 / 36   ≈  69.4 %

Jan 30, 2021