Setting up a matrix with word problems

[Workout]

Homework Statement

A florist offers three sizes of flower arrangements containing roses, daisies,
and chrysanthemums.
Each small arrangement contains one rose, three daisies, and three chrysanthemums.
Each medium arrangement contains two roses, four daisies, and six chrysanthemums.
Each large arrangement contains four roses, eight daisies, and six chrysanthemums.
One day, the florist noted that she used a total of 24 roses, 50 daisies, and 48 chrysanthemums in filling orders for these three types of arrangements.
How many arrangements of each type did she make?

I'm sort of confused on how to set these equations up... like what do they = to?
Let x = roses, y = daises, z = chrysanthemums

Small arrangement: 1x + 3y + 3z = ??
Medium arrangement: 2x + 4y + 6z = ??
Large arrangement: 4x + 8y + 6z = ??
Restriction: 24x + 50y + 48z = ??

Im not sure what these equal to. If I could figure that out maybe I could set a matrice and solve..

 

[Dick]

Homework Statement

A florist offers three sizes of flower arrangements containing roses, daisies,
and chrysanthemums.
Each small arrangement contains one rose, three daisies, and three chrysanthemums.
Each medium arrangement contains two roses, four daisies, and six chrysanthemums.
Each large arrangement contains four roses, eight daisies, and six chrysanthemums.
One day, the florist noted that she used a total of 24 roses, 50 daisies, and 48 chrysanthemums in filling orders for these three types of arrangements.
How many arrangements of each type did she make?

I'm sort of confused on how to set these equations up... like what do they = to?
Let x = roses, y = daises, z = chrysanthemums

Small arrangement: 1x + 3y + 3z = ??
Medium arrangement: 2x + 4y + 6z = ??
Large arrangement: 4x + 8y + 6z = ??
Restriction: 24x + 50y + 48z = ??

Im not sure what these equal to. If I could figure that out maybe I could set a matrice and solve..

Why don't you back up a bit? Put x, y and z to be the things you actually want to solve for. Let x=number of small arrangements, y=number of medium arrangements and z=number of large arrangements. What equations do you get then?

 

[Workout]

ok starting simple.. how do I break down the roses, daisies, and chrysanthemums in the small arrangement which is "x"? Like how would I denote each of these three.

 

[Dick]

ok starting simple.. how do I break down the roses, daisies, and chrysanthemums in the small arrangement which is "x"? Like how would I denote each of these three.

Each small contains 1 rose, each medium contains 2 roses, each large contains 4 roses. What are the number of total roses in terms of x, y and z? You know the total is 24, right? What equation does that give you? Choosing the variable x to be the number of roses is useless. You already know the total number of roses.

 

[Workout]

Ok I got the answer. Thank you!