Homework Help Forum: MATH!

Posted by hmmm... on Monday, November 2, 2009 at 8:12pm.

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 [ | ]

• MATH! - Reiny, Monday, November 2, 2009 at 8:45pm

  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.

  
  

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