Math 302: Habits Of Mind

Timmatha Gagner, McKenna Townsend, Rebecca Hamilton
Math 302- Habits of Mind 1

For Habits of Mind Problem 1, we were given the ratios of carnations to daisies, roses to peonies, and peonies to carnations. We were asked to find the remaining ratios of flowers, which would be peonies to daisies, carnations to roses, and roses to daisies. Madison also wants to give her teacher a bouquet using appropriate ratios and whole flowers. So, for this question we were asked how many of each type of flower should be put in the bouquet. The ratios we were already given are represented in tables 1.1, 1.2 and 1.3

Table 1.1
Carnations
14
28
42
56
70
Daisies
7
14
21
28
35
Note that 14:7 simplifies to 2:1

Table 1.2
Roses
3
6
9
12
15
Peonies
5
10
15
20
25

Table 1.3
Peonies
2
4
6
8
10
Carnations
5
10
15
20
25

We decided to find the ratio between peonies and daisies first because we were given ratios for each of them to carnations (table 1.1 and 1.3). In order to do this we compared the two tables of carnations to daisies (table 1.1) and peonies to carnations (table 1.3).

Following the same steps, we found that we had ratios comparing roses and daisies to carnations. We remembered when comparing carnations to daisies our ratio of 14:7 simplified to 2:1. Knowing this, we went to our table of carnations to roses (table 1.6) and went to the first even number, since odd numbers in a 2:1 ratio would make a half of a flower. Our first even ratio of carnations to roses was 50:12. Since our ratio of carnations to daisies is 2:1, an equivalent ratio to that would be 50:25. This would mean for every 50 carnations, we would have 12 roses and 25 daisies. With this information we were able to conclude our rose to daisy ratio is 12:25. Again, we are not able to simplify this ratio because the only common factor between 12 and 25 is 1. Below is table 1.7 showing more equivalent rose to daisy