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?

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