Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
An employee at a construction company is ordering interior doors for some new houses that are being built. There are 3 one-story houses and 6 two-story houses on the west side of the street, which require a total of 93 doors. On the east side, there are 8 one-story houses and 2 two-story houses, which require a total of 94 doors. Assuming that the floor plans for the one-story houses are identical and so are the two-story houses, how many doors does each type of house have?
Each one-story house has___ doors, and each two-story house has___ doors.
+128408 An employee at a construction company is ordering interior doors for some new houses that are being built. There are 3 one-story houses and 6 two-story houses on the west side of the street, which require a total of 93 doors. On the east side, there are 8 one-story houses and 2 two-story houses, which require a total of 94 doors. Assuming that the floor plans for the one-story houses are identical and so are the two-story houses, how many doors does each type of house have?
Call the number of doors on the one story house = O
Call the number of doors on the two story house = T
So
3O + 6T = 93 dividie this trough by 3 ⇒ O + 2T = 31 (1)
8O + 2T = 94 (2)
Subtract (1) from (2) and we get that
7O = 63
O = 63/7 = 9 doors on the one story house
And using (1)
9 + 2T = 31
2T =31 - 9
2T =22
T =22/2 = 11 doors on the two story house
