An employee at a construction company is ordering interior doors for some new houses that are being built. there are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors. on the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors. assuming that the floor plans for one-story houses are identical and so are the two-story houses, how many doors does each type of house have?

Question

Grayson Huber

Mathematics

21 January, 17:21

An employee at a construction company is ordering interior doors for some new houses that are being built. there are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors. on the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors. assuming that the floor plans for one-story houses are identical and so are the two-story houses, how many doors does each type of house have?

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Sunshine · Answer 1

This is a system of equations, let's set it up. I set the variable for 1 story houses to x and 2 story houses to y. Here are the two equations:

6x + 2y = 72

5x + 7y = 124.

Now we multiply the equations so that when we add them together one of the variables will be cancelled out. I am going to multiply the top equation by 7 and the bottom equation by - 2. This gives us

42x + 14y = 504

-10x - 14y = - 248

Add the two equations together:

32x = 256

Divide by 32 to get x = 8. The one story houses have 8 doors. We can plug this number into one of the original equations and solve for y now. I'm going to use the first equation.

(6*8) + 2y = 72

Now we solve for y

y = 12 So, the 1 story houses have 8 doors and the 2 story houses have 12 doors.