Setting up a matrix with word problems

• Workout
In summary, the florist made 3 small, 3 medium, and 3 large arrangements containing a total of 24 roses, 50 daises, and 48 chrysanthemums.
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..

Workout said:

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?

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.

Workout said:
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.

Ok I got the answer. Thank you!

1. How do I set up a matrix with word problems?

To set up a matrix with word problems, you first need to identify the variables and their corresponding values in the word problem. Then, you can create a matrix by writing the variables in the first row and the values in the second row. If there are multiple equations, you can add more rows to the matrix.

2. What is the purpose of setting up a matrix with word problems?

The purpose of setting up a matrix with word problems is to organize the information given in the word problem and make it easier to solve. By representing the problem in a matrix, you can use mathematical operations to find the solution.

3. How do I know when to use a matrix to solve a word problem?

You can use a matrix to solve a word problem when it involves multiple variables and equations. Setting up a matrix can also be helpful when solving systems of equations or when looking for patterns in a problem.

4. Can a matrix be used to solve any type of word problem?

No, a matrix can only be used to solve certain types of word problems. It is most commonly used for problems involving linear equations and systems of equations. Some word problems may require other methods of solving, such as substitution or elimination.

5. Are there any tips for setting up a matrix with word problems?

One tip for setting up a matrix with word problems is to carefully read and understand the problem before creating the matrix. It can also be helpful to label the variables and equations in the matrix to avoid confusion. Additionally, double-checking the matrix and solution can help ensure accuracy.

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