A florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums. Each small arrangement contains one rose, four daisies, and four chrysanthemums. Each medium arrangement contains two roses, four daisies, and five chrysanthemums. Each large arrangement contains four roses, six daisies, and six chrysanthemums. One day, the florist noted that she used a total of 24 roses, 44 daisies, and 47 chrysanthemums in filling orders for these three types of arrangements. How many arrangements of each type did she make

The number of arrangements she made was:

2 small arrangements

3 medium arrangements

4 large arrangements

Step-by-step explanation:

There are 3 sizes of arrangement

Let r = roses

d = daisies

c = chrysanthemums

Each small arrangement contains one rose, four daisies, and four chrysanthemums.

r + 4d + 4c

Each medium arrangement contains two roses, four daisies, and five chrysanthemums.

2r + 4d + 5c

Each large arrangement contains four roses, six daisies, and six chrysanthemums.

4r + 6d + 6c

We are told that

One day, the florist noted that she used a total of 24 roses, 44 daisies, and 47 chrysanthemums in

Rearranging the equations,

Where s = small arrangements

m = medium arrangements

l = large arrangements

we have:

s + 2m + 4l = 24 ........Total number of roses

3s + 4m + 8l = 50 ....... Total number of daisies

3s + 6m + 6l = 48 ......... Total number of Chrysanthemums

From the above:

We can see that we have 3 equations and to solve it, we use Matrix method to solve this question because this is a 3 system (3 × 3) Matrices

I am unable to type the Matrices solution here, so please find it attached to this answer.

The number of arrangements she made was:

2 small arrangements

3 medium arrangements

4 large arrangements