167. Said Harry to Dick, My purse and money together are worth 16 dollars, but the money is worth 7 times as much as the purse; how much money was there in the purse? and what is the value of the purse?

168. A man being asked the price of his horse, answered, that his horse and saddle together were worth 100 dollars, but the horse was worth 9 times as much as the saddle; what was each worth?

169. A man having a horse, a cow, and a sheep, was asked what was the value of each. He answered, that the cow was worth twice as much as the sheep, and the horse 3 times as much as the sheep, and that all together were worth 60 dollars; what was the value of each?

170. A man bought an apple, an orange, and a melon, for 21 cents; for the orange he gave twice as much as for the apple, and for the melon he gave twice as much as for the orange; how much did he give for each?

171. If 80 dollars' worth of provision will serve 20 men 24 days, how many days will 100 dollars' worth of provision serve 30 men?

172. There is a pole and under water, and 10 feet out; how long is the pole ?

173. In an orchard of fruit trees, of them bear apples, of them bear plums, of them pears, 7 of them peaches, and 3 of them cherries; how many trees are there in the whole, and how many of each Bort?

174. A farmer being asked how many sheep he had, answered, that he had them in 4 pastures; in the first he had of his flock; in the second ; in the third; and in the fourth 15; how many sheep had he?

175. A man driving his geese to market, was met by another, who said, Good-morrow, master, with your

hundred geese; says he, I have not a hundred; but if I had half as many more as I now have, and two geese and a half, I should have a hundred; how many had be?

176. What number is that, to which if its half be added the sum will be 60?

177. What number is that, to which if its third be added the sum will be 48?

178. What number is that, to which if its fifth be added the sum will be 54?

179. What number is that, to which if its half and its third be added the sum will be 55?

180. A man being asked his age, answered, that if its half and its third were added to it, the sum would be 77; what was his age?

181. What number is that which being increased by its half, its fourth, and eighteen more, will be doubled?

182. A boy being asked his age, answered, that if and of his age, and 20 more, were added to his age, the sum would be 3 times his age. What was his age?

183. A man being asked how many sheep he had, answered, that if he had as many more, as many more, and 24 sheep, he should have 100. How many had he?

11 times 3 9 times 3 2 times 11 11 times

No. 29. 5 5 times 2

EXPLANATION OF THE TABLES.—These Tables are designed not for study, but for an accompanying exercise to the usual recitation. By their use, many words will be saved, as the teacher will not be obliged to ask the questions; and hence more can be accomplished in a given time. By substituting and for times and in, Addition can also be reviewed; by substituting from, and mentioning the smaller number first, Subtraction. In

many ways can the tables be used to advantage. The columns can be added, or the numbers added across the tables. The divisor of one number can be subtracted from the dividend of another, or the dividend of one number can be divided by the divisor of another. For example, take Nos. 1.and 7: 11 from 70, 4 from 27, 10 from 121, 3 from 16; or 11 in 70, 4 in 27, 10 in 121, 8 in 16.

ARITHMETIC.

PART II.

KEY.

THE Key contains remarks on the principles employed and illustrations of the manner of solving the examples ir each section. All the most difficult of the practical examples are solved in such a manner as to show the principles by which they are performed.

Instructors who may never have attended to fractions need not be afraid to undertake to teach this book. The author flatters himself that the principles are so illustrated, and the processes are made so simple, that any one, who shall undertake to teach it, will find himself familiar with fractions before he is aware of it, although he knew nothing of them before; and that every one will acquire a facility in solving questions which he never before possessed.

The reasoning used in performing these small examples is precisely the same as that used upon large ones. And when any one finds a difficulty in solving a question, he will remove it much sooner, and much more effectually, by taking a very small example of the same kind, and observing how he does it, than by recurring to a rule.

The practical examples at the commencement of each section and article are generally such as to show the pupil what the combination is, and how he is to perform it. Thus the pupil will learn gradually to reason upon abstract numbers. In each combination, there are a few abstract examples without practical ones, to exercise the pupil in the combinations, after he knows what these combinations are. It would be an excellent exercise for the pupil to put these into a practical form when he is reciting. For instance,