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28 September, 23:12

The ratio of the number of long term parking spaces to the number of short term parking spaces in Farmington Airport is 5 to 7. The ratio of the number of short term parking spaces to the number of parking spaces in the cell phone parking is 8 to 9. There is the total of 3180 parking spaces at the airport. How many parking spaces in the cell phone parking are there?

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  1. 28 September, 23:15
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    1,260

    Step-by-step explanation:

    Let's name

    LT = number of long term parking spaces

    ST = number of short term parking spaces

    CP = the number of parking spaces in the cell phone parking

    We have

    LT/ST = 5/7

    ST/CP = 8/9 or CP/ST = 9/8

    LT + ST + CP = 3180

    Dividing the last equation by ST we get

    LT/ST + 1 + CP/ST = 3180/ST

    replacing

    5/7 + 1 + 9/8 = 3180/ST

    Solving for ST we obtain ST = 1,120.

    Replacing in the second equation, we get CP/1,120 = 9/8,

    hence CP = 1,260
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