5lb book, Chapter 20, #27

[howaboutyes]

"David received a fifth the number of chocolates that Fouad did, [...]"

I believe that D = (1/5)F (or 5D=F), with D denoting number of chocolates received by David and F for Fouad's chocolates, respectively. The solution claims the ratio is 1:5, D:F, D=5F. Either way, together they have 6x chocolates. That 6x = 0.2 times the total number of chocolates. So the total number is 30x, so we're dealing with at least 30 chocolates. That means Stina has 24x, David has 5x, and Fouad has 1x, according to me, and, according to the book, Fouad has 5x and David has 1x.

I think the ratio of the number of chocolates Stina received to the number that David received is 24:5. The book says 24:1. I've had my adviser/professor look over the language, and he scratches his head as well, thinking that I might be in the right. Please help me understand this one -- I don't want to misunderstand something inchoate, and I seem to have similar issues with other language used in the book.

For example, Chapter 27, #20 has that "BC is 1/3 the length of AB," which I interpret to mean BC = (1/3)AB or 3BC = AB. The book says it's 3AB = BC... which makes me terribly confused.

Thank you.

[tommywallach]

Hey David,

Let's do it with numbers.

We're going to be dealing with 80 percent and 1/6, so let's make our total 30.

80 percent = 24 chocolates.

That leaves 6 chocolates:

David gets 1 chocolate
Fouad gets 5 chocolates

So the ratio of Stina to David is 24:1.

Your brain switched things. Remember, if 5D = F, then F is BIGGER than D.

As for the other question, yes BC = 1/3AB, so 3BC = AB. Again, that means that AB is bigger than BC, because you need 3 "BCs" to make 1 "AB" (Which is why they use 3x for AB and x for BC).

Neither of these are errors in the book. Instead, they are errors in your understanding of ratios. If that has your tutor scratching his head, you may need a new tutor! : )

-t

[howaboutyes]

Thanks for the quick reply.

Let me test my understanding, then...
For example, (1/20)H = 2D means that for every "D" we have, we would need 40 "H." So the ratio from H to D is 40:1. Similarly, if 20M = 10P = (1/40)K, we have K = 400P = 800M, so we have a ratio from K to P to M that is 800:400:1. Let me know if I've got it!

Thanks.

[tommywallach]

Hey Howabout,

Yep! If 1/20H = 2D, then H = 40D. That means that H is 40 times bigger than D (you would need 40Ds to equal one H). So the ratio of H to D is 40:1 (in terms of size).

-t