HELPPP!!!! Error in Word Problem Guide page 35???

[lanyunxi]

On page 35 of Word problems guide,

"If Kelly received 1/3 more votes than Mike in a student election, which of the following could have been the total number of votes cast for the two candidates?
a)12
b)13
c)14
d)15
e)16

If we say that M equals the number of votes case by Mike, then how would we represent the number of votes cast for Kelly?

Kelly equals Mike’s votes plus another 1/3 of Mike’s votes, or M + (1/3)M = (4/3)M.

If the question asks us something about the total number of votes cast for Mike and Kelly, what do we know? We can represent the total votes as M + (4/3)M = (7/3)M. (That is, Mike’s votes plus Kelly’s votes = total votes.)

Interesting. Can you figure out anything of significance from that?

The total number of votes must be a multiple of 7. Why? Well, the number of votes must be an integer (hidden constraint!), and whatever that number is, it equals 7M/3. There isn’t a 7 on the bottom of the fraction, so that 7 on top can never be cancelled out. It’s always there… so, whatever the total number of votes is, it’s a multiple of 7. (If you’re not sure why, play around with some real numbers that fit this pattern. Prove it to yourself.)

What else? Turns out, M has to be a multiple of 3. Again, that total number of votes must be an integer. In order for that to be true, that denominator has to disappear somehow. It isn’t going to be cancelled out by the 7, so it must get cancelled out by something in the M. That M, then, must contain a 3."


THe above is the explanations given on the book.
However,
1) isn't 7 the numerator on the top, and not a denominator???
2) if 7 is the numerator and 3 is the denominator, then shouldn't answer be either 12 or 15??? as they both are multiples of 3. In other words, can be divided?


HELPPPPPP

[tommywallach]

Hey There,

I CAN HELP!!!!!

Here are your questions:

1) isn't 7 the numerator on the top, and not a denominator???

Answer #1: Hmm. Nothing in the text ever said that the 7 is in the denominator, so I'm not sure where you're getting that. What they say is that there is a 7 in the numerator and there isn't a 7 in the denominator. That means the 7 won't get cancelled (the 3 can't cancel out the 7). Since we know the total number of votes will 7M/3, it will definitely be a multiple of 7 (because it can't be a non-integer).

2) if 7 is the numerator and 3 is the denominator, then shouldn't answer be either 12 or 15??? as they both are multiples of 3. In other words, can be divided?

Don't forget, we know that M is a multiple of 3, not the total number of votes. The second point made in that explanation is unnecessary. Once we know it has to be a multiple of 7, we already know the answer. Now M has to be a multiple of 3, but our answer is 7M/3. So if M were 3, then the total votes would be 7. If M were 6, then the total votes would be 14.

Did I help?

-t