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155. If the wages of 25 weeks come to 75 dollars, what will be the wages of 7 weeks ?
156. If 8 tons of hay will keep 7 horses three months, how much will keep 12 horses the same time ?
157. If a staff 4 feet long cast a shadow 6 feet long, what is the length of a pole that casts a shadow 58 feet at the same time of day?
158. If a stick 8 feet long cast a shadow 2 feet in length, what is the height of a tree which casts a shadow 42 feet at the same time of day? 159. At 6 dollars per week, how
months' board can I have for 100 dollars ?
160. A ship has sailed 24 miles in 4 hours ; how long will it take her to sail 150 miles at the same rate ?
161. 30 men can perform a piece of work in 20 days; how many men will it take to perform the same work in 8 days ?
162. 17 men can perform a piece of work in 25 days; in how many days would 5 men perform the same work?
163. A hare has 76 rods the start of a greyhound, but the greyhound runs 15 rods to 10 of the hare ; how
many rods must the greyhound run to overtake the hare ?
164. A garrison has provision for 8 months, at the rate of 15 ounces per day ; how much must be allowed per day, in order that the provision may last 11 months ?
165. If 8 men can build a wall 15 rods in length in 10 days, how many men will it take to build a wall 45 rods in length in 5 days?
166. If a quarter of wheat affords 60 ten-penny loaves, how many eight-penny loaves may be obtained from it?
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 į and f under water, and 10 feet out; how long is the pole?
173. In an orchard of fruit trees, 1 of them bear apples, 1 of them bear plums, šof them pears, 7 of them peaches, and 3 of them cherries; how many trees are there in the whole, and how
of each sort?
174. A farmer being asked how many sheep he had, answered, that he had them in 4 pastures; in the first he had į of his flock; in the second _ ; in the third t ; 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 hun. dred; how many had he ?
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 to 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 į and I of his age, and 20 more were added to his age, the sum would be 3 times his age.
his age ?
183. A man being asked how many sheep he had, answered, that if he had as many more, 1 as inany more, and 21 sheep, he should have 100. How
many had he
The Key contains remarks on the principles employed and ilustrations of the manner of solving the examples in 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. Care has been taken to select examples for solution, that will explain those which are not solved. Many remarks with regard to the manner of illustrating the principles to the pupils are inserted in their proper places.
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. This will learn the pupil gradually to reason upon abstract numbers. In each combination, there are a few abstract examples without practical ones, to exercise the learner in
the combinations, after he knows what these combinations
It would be an excellent exercise for the pupil to put these into a practical form when he is reciting. For instance when the question is, how many are 5 and 3? Let him make a question in this way; if an orange cost five cents, and an apple 3 cents, what would they both come to? This may be done in all cases.
The examples are often so arranged, that several depend on each other, so that the preceding explains the following one. Sometimes also, in the same example, there are several questions asked, so as to lead the pupil gradually from the simple to the more difficult. It would be well for the pupil to acquire the habit of doing this for himself, when difficult questions occur.
The operations can be illustrated by counters, or marks on the blackboard, according to the necessity of the pupils, These illustrations will be less necessary 18 the pupils advance in the work; but a frequent reference to them throughout most of the book will be useful in fixing more clearly in mind the principles involved in the operations.
The book may be used in classes where it is convenient. The pupil may answer the questions with the book before him or not, as the instructor thinks proper. A very useful mode of recitation is for the instructor to read the example to the whole class, and then, allowing sufficient time for them to perform the question, call upon some one to answer it. In this manner every pupil will be obliged to perform the example, because they do not know who is to answer it. In this way it will be best for them to answer without the book.
It will often be well to let the elder pupils hear the younger. This will be a useful exercise for them, and an assistance to the instructor.
A. This section contains addition and subtraction. The first example may be solved by means of beans, peas, &c., or by means of the blackboard. The former method is