The puzzle says there are 500 members in the club now. Some are old members, some are new. You don’t know how many of each. The only thing you know is that 70% of the old members continued to stay in the club.
The answer says that because 70% of $20 is $14, and 70% of the old members stayed, the average payment by old members is $14. I understand and agree with that. But the total they paid varies depending on how many there were.
Suppose there WERE 710 old members. If 70% of them rejoined, that would mean 497 rejoined and 3 new members joined. Each returning members paid $20 and new members paid $14. 20497 + 314 = 9982. This is not the $7000 claimed in the answer. The average paid by old members is $14, as stated.
Similarly, if there were 690 old members and 70% rejoined, that would be 483 rejoining. 48320 + 1417 = 9898. Again, the average payment for ALL old members is $14, but that isn’t the average payment for those that stayed.
While it is true that 70% of the long term members paying $20 is the same as all old members paying $14, the number of long term members returning depends on how many new members there are.
So yes, 49720 = 71014, but that doesn’t really help with the way the puzzle was worded.
I don’t see it, anyway. Anyone care to try and explain it to me?
That almost makes sense, but 70% of 483 is 338.1 That means either 338 stayed or 339, we don’t know if we need to take the floor or ceiling.
If 338 stayed, 338 * 20 + 238 = 6998
If 339 stayed, 339 * 20 + 238 = 7018
So unless the 70% is guaranteed to come out a whole number by some other rule I missed, I don’t think you can give an exact count, just a good approximation.
For example, lets assume there were 400 old and 100 new.
100 * 14 = 1400 from new
(400 * .7) * 20 = 5600 from old
That’s true, but I think you’re overthinking it; “the 70% is guaranteed to come out a whole number” only in the sense that that’s what actually happened. We know the number of old members does happen to fit that bill: maybe it’s 10, and 7 of them pay; maybe, as you say, it’s 400, and 280 of them pay; we never find out, but we don’t need to so narrow it down; whatever the actual number is, we’re already told that it’s one of the ones that works.
Almost. It’s guaranteed to come out as a whole number because people come in whole numbers. It’s guaranteed that a whole number of people will buy tickets–you can’t have .13 person buying a ticket. What’s not guaranteed is that the percentage will be nice and round like 70%.
Reality gives you the whole number. The problem gives you the conveniently round percentage :).