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