There are cars, trucks, and motorcycles in our company parking lot. the ratio of cars to trucks to motorcycles is $7: 5: 2.$ if there are $48$ cars and trucks total, how many motorcycles are there?

Given the ratio of cars, trucks and motorcycles 7:5:2 and the total number of cars is 48, to get the number of motorcycles we proceed as follows:
fraction of cars to total number
(5+7)/(7+5+2)
=12/14
=6/7
the total number of cars, trucks and motorcycles will be:
1/(6/7)×48
=56
total number motorcycles
2/14*56
=8 motorcycles