##### Aug 06, 2016

**RAY**: It’s been a well-kept secret, but there exists a Car Talk Social Club which has 500 members in it now. We used to have 5,000 but we've had a little problem attracting members lately.

For our upcoming celebration we decided that to offer new members tickets at a discount to get them to come --14 dollars a ticket. But long-term members would be charged 20 dollars each for their tickets. Not surprisingly all the new members buy the 14-dollar tickets. But only 70-percent of the long-term members fork over the 20 bucks. Cheapskates!

Now here's the deal. You don't know how many new members or long-term members there are. I just said we had 500 overall members. But you do know that 70-percent of the old members showed up, 30-percent of the old members didn't show up, and all of the new members showed up.

The question is how much money did we collect?

Answer:

**RAY**: It turns out that 70-percent of 20 is 14. So, 70-percent of the long-term members paying 20-bucks each is exactly equivalent to 100-percent of the long-term members paying 14-dollars each.

So, you don't have to know how many long-term and how many new members there were. It's just as if all 500 members paid 14-dollars for a ticket. If you wrote an algebraic expression, you would see that R for revenue equals 14N, with N as the new members, plus 20, which is what we're charging the geezers times .7, which is 70-percent, times 500 minus N.

And, if you do that math, it turns out to be R, or revenue, equals 14 times 500, or 7,000. So we took in 7,000 bucks.

**TOM**: Well, where's my half?

**RAY**: I sent it to you. You didn't get it? So who's our winner this week?

**TOM**: The winner this week is John Ridgway from Greenfield, Massachusetts. Congratulations!