8. Bought 60 yards of cloth at the rate of 2 yards for $5, and 80 yards more at the rate of 4 yards for $9. I immediately sold the whole of it at the rate of 5 yards for $12. How much did I gain? 9. A man purchased 40 bushels of apples at $1.50 per bushel. Twenty-five hundredths of them were damaged, and he sold them at 20 cents per peck. He sold the remainder at 50 cents per peck. How much did he gain or lose? 10. If oranges are 37-1/2 cents per dozen, how many boxes, each containing 480, can be bought for $60? 11. A man can do a piece of work in 18-3/4 days. What part of it can he do in 6-2/3 days? 12. How old to-day is a boy that was born Oct. 29, 1896? [Walsh, '06, Part I, p. 165.] As a result, teachers and textbook writers have come to think of the functions of solving arithmetical problems as identical with the function of solving the described problems which they give in school in books, examination papers, and the like. If they do not think explicitly that this is so, they still act in training and in testing pupils as if it were so. It is not. Problems should be solved in school to the end that pupils may solve the problems which life offers. To know what change one should receive after a given real purchase, to keep one's accounts accurately, to adapt a recipe for six so as to make enough of the article for four persons, to estimate the amount of seed required for a plot of a given size from the statement of the amount required per acre, to make with surety the applications that the household, small stores, and ordinary trades require--such is the ability that the elementary school should develop. Other things being equal, the school should set problems in arithmetic which life then and later will set, should favor the situations which life itself offers and the responses which life itself demands.