study island/ ratios and proportions

Question

Michelle is planting flowers in her garden. She wants the ratio of daisies to carnations to be 3 to 2. Michelle wants to plant a total of 35 flowers. How many daisies should she plant?



Answer 1

How many daisies should Michelle plant is the solution we are searching for, in other words, you must determine the exact amount of the proportion of daisies to carnations.

First Fact: There are 3 daisies for every 2 carnations. Knowing this we can deduce that there are 5 flowers in each portion of flowers.

Second Fact: There are going to be a total of 35 flowers in the entire garden. Therefore, combining this information with the deduction of the 1st fact, we can conclude that there are 7 portions or groups of flowers containing 5 flowers each, and those 5 flowers are going to be 3 daisies and 2 carnations. [The math for this thought process would be as follows: 35 flowers in garden x (1 portion of flowers / 5 flowers) = 35 / 5 = 7 portions or groups of flowers in sets of 5.]

The equation to solve is: 3 daisies x 7 portions or groups = 21 daisies

Michelle should plant 21 daisies and 14 carnations, so her garden will have 35 flowers in total with a ration of daisies to carnations being 3/2 or 3:2 or (3 to 2).

Answer 2

A part-to-whole ratio can be written to solve this problem. We can create a pair of equivalent ratios for the number of daisies to the total number of flowers for each situation, using x as the number of daisies for the ratio that uses the 35 total flowers.

Since the ratio of daisies to carnations is 3 to 2, we can say that the ratio of daisies to total is 3 to 5.

Then, we can write a pair of equivalent ratios as:

3 daisies / 5 total flowers = x daisies / 35 total flowers

Since 5 * 7 = 35 , we can multiply 3 * 7 to find the total number of daises for a group of 35 total flowers:

3 * 7 = 21 daisies

3/5 = 21/35

Answer 3

A part-to-whole ratio can be written to solve this problem. We can create a pair of equivalent ratios for the number of daisies to the total number of flowers for each situation, using x as the number of daisies for the ratio that uses the 35 total flowers.

Since the ratio of daisies to carnations is 3 to 2, we can say that the ratio of daisies to total is 3 to 5.

Then, we can write a pair of equivalent ratios as:

3 daisies / 5 total flowers = x daisies / 35 total flowers

Since 5 * 7 = 35 , we can multiply 3 * 7 to find the total number of daises for a group of 35 total flowers:

3 * 7 = 21 daisies

3/5 = 21/35