There are 22 roses, 12 daisies, and 16 carnations in a bouquet. what is the ratio of roses to the total number of flowers in the bouquet? how many carnations must be added to the bouquet so that the ratio of daisies to carnations becomes 1: 3?

Given:
Roses:       22
Daisies:     12
Carnation: 16

22 + 12 + 16 = 50 flowers in one bouquet

The ratio of the roses to the total number of flowers in the bouquet is 22/50 or simplified to 11/25

Ratio of daisies to carnations is 12:16 or 3:4. 

Number of carnations to add to make the ratio into 1:3

12:x = 1:3
12*3 = x
36 = x

36 - 16 = 20 additional carnations.

There must be an additional 20 carnations to make the ratio of daisies to carnation 1:3.

12:36 = 1:3

Agc and bgd are vertical angles