Page:Carroll - Tangled Tale.djvu/123

Rh CLASS LIST.

Problem 2.—L makes 5 scarves, while M makes 2: Z makes 4 while L makes 3. Five scarves of Zs weigh one of Ls; 5 of Ms weigh 3 of Zs. One of Ms is as warm as 4 of Zs: and one of Ls as warm as 3 of Ms. Which is best, giving equal weight in the result to rapidity of work, lightness, and warmth?

Answer.—The order is M, L, Z.

Solution.—As to rapidity (other things being constant) Ls merit is to Ms in the ratio of 5 to 2: Zs to Ls in the ratio of 4 to 3. In order to get one set of 3 numbers fulfilling these conditions, it is perhaps simplest to take the one that occurs twice as unity, and reduce the others to fractions: this gives, for L, M, and Z, the marks 1, $2⁄5$, $4⁄3$. In estimating for lightness, we observe that the greater the weight, the less the merit, so that Zs merit is to Ls as 5 to 1. Thus the marks for lightness are $1⁄5$, $5⁄3$, 1. And similarly, the marks for warmth are 3, 1, $1⁄4$. To get the