A parking lot has spaces reserved for motocyles, cars and vans. There are five more spaces reserved for vans than motorcycles. There are three timea as many car spaces as van and motorcycle spaces combined. If the parking lot has 180 total reserved spaces how many of each type are there?

motorcycles: 20 vans: 25 cars: 135

Step-by-step explanation:

There are 3 car spaces for each non-car space, so the number of car spaces is 3/4 of the total: (3/4) * 180 = 135.

The number of motorcycle spaces is half of 5 less than the remainder, so is ...

(180 - 135-5) / 2 = 20

and van spaces are 5 more than that: 25.

There are 20 motorcycle spaces, 25 van spaces, and 135 car spaces.