At the gym, 371 people lift weights, 514 swim, 489 play tennis. Of the above, 177 lift weights and swim, 179 lift and play tennis, 184 swim and play tennis, 177 swim and lift. 100 people lift, swim and play tennis. 89 dont use the gym at all. How many people belong to the gym?

Add the number of people who lift weghts, swim, and play tennis in the gym: 371 + 514 + 489 = 1374.

However, the people who engage exactly in two activities were counted twice and the people who do all three of them were counted thrice. To obtain the correct answer we need to subtract the numbers 177, 179, 184 and then add the number 100: 1374 - (177 + 179 + 184) + 100 = 1374 - 540 + 100 = 934.