May 12, 2008
RAY: The kernel of this puzzler was sent in by a fellow named Butch Guest. He gave me permission to rewrite it.
Well, 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. And that 500 includes all of our friends and family members and a few ex-wives.
For our upcoming celebration this year we are going to have our Hawaiian Luau Lambada and Lasagna Extravangaza. We decided that for new members (those who had been members for less than a year), in order to get them to attend, we would offer tickets at a discount --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?
Well, 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. And that 500 includes all of our friends and family members and a few ex-wives.
For our upcoming celebration this year we are going to have our Hawaiian Luau Lambada and Lasagna Extravangaza. We decided that for new members (those who had been members for less than a year), in order to get them to attend, we would offer tickets at a discount --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: Here's the answer, and the interesting part. Seventy percent of the long-term members attended the Car Talk Social Club event, because they were ticked off that we were charging 20-bucks a ticket.
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.
TOM: Whatever you say!
RAY: 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 Jean Moore from New Milford, Connecticut. And for having her answer selected at random from all the correct answers that we got, Jean is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, with which she can get a copy of our brand new four CD set with the evocative title Field Guide to the North American Wacko.
RAY: Congratulations Jean!
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.
TOM: Whatever you say!
RAY: 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 Jean Moore from New Milford, Connecticut. And for having her answer selected at random from all the correct answers that we got, Jean is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, with which she can get a copy of our brand new four CD set with the evocative title Field Guide to the North American Wacko.
RAY: Congratulations Jean!
