The Mountain Trail Resort sold 64 condominiums last year, all 1, 2, or 3 bedroom condominiums. The total revenue from the sale of the condominiums was $5,493,000. The combined square footage of all the condominiums sold was 51,544 square feet. One bedroom condominiums sold for $72,000, two bedroom condominiums sold for $87,000, and three bedroom condominiums sold for $102,000. One bedroom condominiums have an area of 512 square feet, two bedroom condominiums have an area of 840 square feet, and three bedroom condominiums have an area of 1120 square feet. How many of each size condominium did Mountain Trail Resort sell last year? Use the matrices A and B below to enter the matrices that you use to solve this problem. Your solution must include a system of equations with a definition of the variables and an explanation of how you solved the problem using matrices.

Question

The Mountain Trail Resort sold 64 condominiums last year, all 1, 2, or 3 bedroom condominiums. The total revenue from the sale of the condominiums was $5,493,000. The combined square footage of all the condominiums sold was 51,544 square feet. One bedroom condominiums sold for $72,000, two bedroom condominiums sold for $87,000, and three bedroom condominiums sold for $102,000. One bedroom condominiums have an area of 512 square feet, two bedroom condominiums have an area of 840 square feet, and three bedroom condominiums have an area of 1120 square feet. How many of each size condominium did Mountain Trail Resort sell last year? Use the matrices A and B below to enter the matrices that you use to solve this problem. Your solution must include a system of equations with a definition of the variables and an explanation of how you solved the problem using matrices.

[ | | ]
[ | | ] =A
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[ | ] =B
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Im not sure where the numbers go...I have been working on this problem for like 5 days plleeeaassee help(:

Answer 1

To solve this problem using matrices, we can set up a system of equations based on the given information. Let's define the variables:

Let x be the number of one-bedroom condominiums sold.
Let y be the number of two-bedroom condominiums sold.
Let z be the number of three-bedroom condominiums sold.

We can now set up the system of equations:

Equation 1: x + y + z = 64 (Total number of condominiums sold)

Equation 2: 72,000x + 87,000y + 102,000z = 5,493,000 (Total revenue from the sale of condominiums)

Equation 3: 512x + 840y + 1120z = 51,544 (Total square footage of all condominiums sold)

Now, we can represent the system of equations using matrices.

Matrix A will represent the coefficients of the variables:
[1 1 1]
[72,000 87,000 102,000]
[512 840 1120]

Matrix X will represent the variables:
[x]
[y]
[z]

Matrix B will represent the constant terms:
[64]
[5,493,000]
[51,544]

Now, let's rewrite the system of equations in matrix form:

A * X = B

Multiply both sides by the inverse of matrix A to solve for X:

X = A^(-1) * B

To solve for X using matrices, you can use matrix algebra software like MATLAB or even online matrix calculators. Input matrices A and B, then calculate the inverse of A using matrix algebra software, and finally multiply the inverse of A by B to get the solution matrix X.

Once you have the solution matrix X, you will have the values for x, y, and z, representing the number of each size condominium sold by Mountain Trail Resort last year.