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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.

 Jan 26, 2021
 #1
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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

 

 

cool cool cool

 Jan 26, 2021

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