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.

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[ | | ] =A
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[ | ] =B
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Answer 1

Since I cannot tell from your post what your matrices are to look like, let's set it up

First of all, your information can be expressed as a system of equations in 3 variables, x, y, and z as the number of 1, 2, or 3 bedroom condos.
so we get
#1: x + y + z = 64
#2: 72x + 87y + 102z = 5493 after dividing by 100, and then further dividing by 3
24x + 29y + 34z = 1831
#3: 512x + 840y + 1120z = 51544
or after dividing by 8
64x + 105y + 140z = 6818
of course you solve these by the old stand-by of elimination, but since it asked for matrix solution, you would set it up as
1 1 1
24 29 34
64 105 140
multiplied by
x
y
x
to get
64
1831
6818
thatis, a 3by3 times a 3by1 to get a 3by1

The most common way, is to find the inverse of the 3by3 and then multiply each side by that inverse.

I don't know if that is the method you have learned.

Answer 2

To solve this problem using matrices, we can set up a system of equations.

Let's define the variables:
x = number of one-bedroom condominiums sold
y = number of two-bedroom condominiums sold
z = number of three-bedroom condominiums sold

We can now set up the equations based on the given information:

Equation 1: x + y + z = 64 (equation for the total number of condominiums sold)

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

Equation 3: 512x + 840y + 1120z = 51,544 (equation for the total square footage of the condominiums sold)

Now, let's enter these equations into the matrix format:

A = [1 1 1; 72000 87000 102000; 512 840 1120]
B = [64; 5493000; 51544]

The matrix equation is obtained by multiplying A with the variables matrix X:

AX = B

Now, to solve for X, we can use matrix inversion:

X = A^(-1) * B

First, we need to find the inverse of matrix A using any suitable method like Gaussian elimination or matrix calculator.

Once you have the inverse of A, you can multiply it with matrix B to get the solution matrix X.

Solving this system of equations using matrices will give us the values for x, y, and z, which represent the number of each size condominium sold by Mountain Trail Resort last year.