The Mountain Trail Resort sold 64 condominiums last year, all 1, 2, or 3 bedroom

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 =



B =

Explanation / Answer

If x is the number of one bedrooms sold, y is the number of two bedrooms sold and z is the number of three bedrooms sold, then the system of equations would be: x+y+z=64 72000x+87000y+102000z=5493000 512x+840y+1120z=51544 Are you studying Kramer's rule for matrices, or matrix multiplication? Or row reducing? I would use row reduction for this situation and say that: [ 1 1 1 72000 87000 102000 512 840 1120] (i just used the coefficients of x, y and z here) times vertical matrix [x y z] Must equal the results [64 5493000 51544] So I get that x= 17 one bedrooms y= 35 two bedrooms z= 12 three bedrooms Hope this helps!

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