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 7 two-story houses on the west side of the street, which require a total of 172 doors. On the east side, there are 6 one-story houses and 4 two-story houses, which require a total of 124 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.
Question
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 7 two-story houses on the west side of the street, which require a total of 172 doors. On the east side, there are 6 one-story houses and 4 two-story houses, which require a total of 124 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.
Solution
Let's solve this problem step by step:
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First, let's denote the number of doors in a one-story house as x and the number of doors in a two-story house as y.
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From the problem, we know that the total number of doors in the one-story and two-story houses on the west side of the street is 172. This can be represented as: 6x + 7y = 172.
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Similarly, the total number of doors in the one-story and two-story houses on the east side of the street is 124. This can be represented as: 6x + 4y = 124.
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Now we have a system of two equations, and we can solve it to find the values of x and y.
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Subtract the second equation from the first to get: 3y = 48, so y = 16.
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Substitute y = 16 into the second equation to get: 6x + 4*16 = 124, so 6x = 60, and x = 10.
So, each one-story house has 10 doors, and each two-story house has 16 doors.
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