The ratio of the number of cars to the number of motorcycles in a parking lot is 10:3. The ratio of the number of motorcycles to the numbers of vans is 2:3. There are 30 vans in the parking lot. How many more cars than vans are there?

I'll do this step-by-step. Note, ratios are basically division signs.

The ratio of cars to motorcycles in a parking lot is 10:3, which means there are 10 cars for every 3 motorcycles.

The ratio of motorcycles to vans is 2:3, there are 2 motorcycles for every 3 vans.

There are 30 vans, so there are 20 motorcycles, since 20 motorcycles:30 vans is equal to 2 motorcycles: 3 vans in fractions. (20 / 30 = 2 / 3)

So, the ratio of cars represented by x to the number of motorcycles, 20 can be written as x / 20 = 10 / 3. 10 / 3 is 3.333, meaning 3.333 cars per 1 motorcycle, so multiply 20 by 3.333 to get x, which is 66. There are 66 cars and 30 vans, so there are 33 more cars than vans in the parking lot. 66/20 = 10/3, both have a ratio of 3.33 when divided.

If you don't want the explanation, there are 33 more cars than vans in the parking lot.