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?

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.