What do you think of the following method for solving a type of probability problem?

People have a difficult time solving probability problems. I read about a useful way of approaching certain problems. I will first give a problem and then outline the approach to solving it. See if it makes sense.

0.8 percent of the population has a certain disease. The test for the disease is positive for 90% of those who have it. For those who do not have it there is a 7% chance of getting a false positive. If someone tests positive, what is their chance of having the disease?

Here is the approach that I read about – no equations and no algebra. Consider a sample size of 1000 patients. How many of them have the disease? Of those people, how many will test positive? Then find how many of the 1000 do not have the disease, and out of that number, how many will test positive. What is the total number that test positive? Of those, how many actually have the disease? To make things easier, round the numbers involved to the neatest whole number.