A and B went to market with 30 pigs each. A sold his pigs at 2 for $1, and B sold his pigs at the rate of 3 for $1, and they, together, received $25. The next day A went to market alone with 60 pigs, and, wishing to sell at the same rate, sold them 5 for $2, and received only $24. Why should he not receive as much as when B owned half of the pigs?
Answer.—The rate of 2 pigs for $1 is 1 pig for $½, and the rate of 3 pigs for $1 is 1 pig for $⅓; the average rate is 2 pigs for $½ + $⅓, or $⅚, or 1 pig for $5/12. The rate of 5 pigs for $2 is 1 pig for $⅖. So it is seen that the reason A did not receive as much is that he sold his pigs at a less rate than when they both went to market.
Two hunters killed a deer and sold it by the pound in the woods. They had no proper means of weighing it, but knew their own weights—one 130 pounds and the other 190 pounds. They placed a rail across a fence so that it balanced with one of them on each end. They then exchanged places, the lighter man taking the deer in his lap, and the rail again balanced; what was the weight of the deer?
Answer.—Let the weight of the deer be denoted by D; then, by the principles of the lever, we have the proportion:
| 130 : 190 | = | 190 : 130 + D: | ||
| Or, | 130 (130 + D) | = | 190 × 190; | |
| Whence, | 16900 + 130 D | = | 36100: | |
| Or, | 130 D | = | 19200; | |
| And, | D | = | 147-9/13. |
Who can solve the following problem?
A hundred and one by fifty divide,
And next let a cipher be duly applied,
And if the result you should rightly divine,
You’ll find that the whole makes but one out of nine.