1. What difference is there between twice 5 and twenty, and twice twenty five 7 Ans. 20. 2. In an orchard of fruit trees + of them bear apples, # pears, # plums, 60 of them peaches, and 40 cherries; how many trees does the orchard contain 7 Ans. 1200. 3. A merchant begins the world with $500, and finds that by his distillery he clears $5000, in 6 years; by his navigation, $5000 in 74 years; and that he spends in gambling $5000 in 3 years; how long will his estate last 7 ** Ans. 30 years. 4. A can do a piece of work alone in 7 days, and B. in 12; in what time will both, working together, finish it ! Ans. 41% days. 5. A. and B. are on opposite sides of a circular field 268 poles about; they being to go round it, both the same way at the same instant of time; A. goes 22 rods in 2 minutes, and B. 34 rods in 3 minutes; how many times will they go round the field before the swifter overtakes the slower 7 Ans }; 164 times. ) B 17 times. 6. A water tub holds 73 gallons; the pipe, which conveys the water to it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes. Now, supposing both these to be carelessly left open, and the water to be turned on at 4 o'clock in the morning : a servant, at 6, finding the water running, puts in the tap: in what time, after this accident, will the tub be filled ? Ans. 32 min. 58+}; sec. 7. A hare starts 12 rods before a hound; but is not perceived by him till she has been up 45 seconds ; she scuds away at the rate of 10 miles an hour; and the dog, on view, makes after her at the rate of 16 miles an hour; how long will the course hold, and what space will be run over, from the spot where the dog started 2 Ans. 2288 ft. 97% seconds. 8. Required the number, from which, if 7 be subtracted, and the remainder be divided by 8, and the quotient be multiplied by 5, and 4 added to the product, the square root of the sum extracted, and three fourths of that root cubed, the cube, divided by 9, the last quotient may be 247 Ans. 103. 9. Suppose a lighthouse built on the top of a rock ; the distance between the place of observation and that part of the rock level with the eye, 620 yards; the distance from the top of the rock to the place of observation, 843 yards; and from the top of the light house 900 yards; the height of the light house is required? . Ans. 76-77+ yils. 10. Sound, uninterrupted, moves at the rate of 1142 feet per second; if the time between the lightning and thunder be one minute. at what distance was the explosion ? Ans. 12.977–H miles. 11. If the earth be 7911 miles in diameter, and the moon 2180 iles; how many moons will it take to make one earth" imlies; y Ans. 47-788. 12. A father left his estate of $1300 per annum to his only scn, but he being only 14 years of age, his guardian was to pay $100 per annum for board, education, &c., and the surplus was to be put out to interest for his benefit, at 6 per cent, compound interest; now allowing no loss, what sum had his guardian to pay him when he was of age 7 Ans. 1115 dols. 33 cts. 5 m. 13. Hiero, king of Sicily, ordered his jeweller to make a crown, containing 63 ounces of gold. The workman thought that substituting part silver was only a proper perquisite, which taking air, Archimedes was appointed to examine it, who on putting it into a vessel of water found it raised the fluid 8-22.45 cubick inches, and having discovered that the inch of gold weighed 10:36 ounces, and that of silver but 5-85 ounces, he found what part of the king's gold had been changed. Repeat the process and inform us what part of it was gold, and what silver? Ans } 28:8038 oz. silver. 34, 1962 oz. gold. 14. A person having driven a stock of cattle to market, received for them all 450 dollars, he was paid at 50 dollars for each horse, 20 dollars for each cow, and 4 dollars for each sheep; the number of cows was double the number of horses; and there were three times as many sheep as cows: what did he receive for the horses, what for the cows, and what for the sheep, and how many of each sort were there 24 Sheep $ 96 Ans. & 8 Cows $160 4 Horses $200 15. A gate-keeper is to receive 6 cents for every wagon, 4 cents for every gig, 2 cents for every horseman, and 1 cent for every footman that passes the gate ; at the year's end he found that 3150 gigs had passed, and that 7 gigs passed when 5 wagons did, and 4 horsemen passed when 6 footmen did, and 5 footmen passed when 3 gigs did, what number of wagons, horsemen, and footmen passed, and how much did the gate-keeper receive? Gigs 3150 - Wagons 2250 * Ans. & Footmen 5250 - Horsemen 3500 Armount of toll $383-50 16. If 1000 bricks lie 6 inches from each other in a straight line, and a person be employed to gather them up one by one, and place them on a pile which is one foot from the first brick, how far will he have walked when he shall have placed the last brick on the pile *s. Ans. 94M. 7 fur. 186yds 2ft. 17. A man dying left his wife in expectation that a child would be afterwards added to the surviving family; and making his will, ordered. that, if the child were a son, 3 of his estate should belong to him, and the remainder to his mother; but if it were a daughter, he appointed the mother #, and the child the remainder. But it happened, that the addition was both a son and a daughter, by which the widow lost in equity, $2400 more than if there had been only a girl. What would have been her dowry had she had only a son ? Ans. $2100. 18. When first the marriage knot was tied Betwixt my wife and me, My age with hers did so agree, As nineteen does with eight and three ; But after ten and half ten years, We man and wife had been, Her age came up so near to mine, As two times three to nine. What were our ages at marriage 7 Ans. 57 and 33. 19. Three jealous husbands with their wives, being ready to pass by night over a river, do find at the water side a boat which can carry but two persons at once, and for want of a waterman, they are necessitated to row themselves over the river at several times: The question is, how those six persons shall pass by 2 and 2, so that none of the three wives may be found in the company of one or two men, unless her husband be present 7 20. As I was going to St. Ives, I met seven wives, Every wife had seven sacks, t Every sack had seven cats, , a. Every cat had seven kits, Kits, cats, sacks and wives, How many were going to St. Ives! 21. A countryman having a Fox, a Goose, and a peck of corn, in his journey, came to a river, where it so happened that he could carry but one over at a time. Now as no two were to be left together that might destroy each other; so he was at his wit’s end how to dispose of them; for, says he, tho’ the corn can't eat the goose, nor the goose eat the fox; yet the fox can eat the goose, and the goose eat the corn. The question is, how he must carry them over that they may not devour each other ? 22. 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 an hundred, but if I had half as many as I now have, and two geese and a half beside the number I now have already, I should have an hundred. How many had he ” 23. Two men were driving sheep to market, says one to the other, give me one of yours and I shall have as many as you; the other says, give me one of yours and I shall have as many again as you. How many had each 7 {After the scholar, male or female, has acquired a competent knowledge of Arithmetick, or of its fundamental rules, instruction in the mode of keeping accounts should be attended to. By this it is not meant to recommend that the son or daughter of every farmer, mechanick, or shop keeper should enter deeply into the science as practised by the merchant, engaged in extensive business, for such study would engross a great portion of time which might be more usefully employed in acquiring a proper knowledge of a trade or other employment. Persons employed in the common business of life, who do not keep regular accounts, are subjected to many losses and inconveniences; to avoid which, the following simple and correct plan, is recommended for their adoption. Let a small book be made, or a few sheets of paper sewed together, and ruled after the examples given in this system. In the book, termed the Day Book, are duly to be entered, daily, all the transactions of the master or mistress of the family, which require a charge to be made, or a credit to be given to any person. No article thus subject to be entered, should on any consideration, be deferred till another day. Great attention should be given to write the transaction in a plain hand; the entry should mention all the particulars necessary to make it fully understood with the time when they took place; and if an article be delivered, the name of the person to whom delivered is to be mentioned. No scratching out may be suffered; because it is sometimes done for dishonest purposes, and will weaken or destroy the authority of your accounts. But if, through mistake, any transaction should be wrongly entered, the error must be rectified, by a new entry i and the wrong one may be cancelled by writing the word Error, in the margin. A book, thus fairly kept, will at all times show the exact state of a person's affairs, and have great weight, should there at any time be a necessity of producing it in a court of Justice. The instructer, who feels a parental solicitude for the permanent welfare of his pupils, cannot in any way so much contribute to their success in life, with so little trouble, as to teach them to understand this abridged, complete and simple system of Book-KeepingIt contains all the important principles of extended and expensive works on the science; all, in fact, that is necessary to be known by the Farmer, Mechanick, and Shopkeeper, relating to accounts; and yet with very little explanation and repeated copying and balancing the accounts, will be so fully understood and deeply impressed on the memory of scholars of common mind, as never to be forgotten ; while their knowledge of common arithmetick and practisal penmanship will thereby be greatly improved.] . Book-KEEPING is the art of recording mercantile transactions in a regular and systematick manner. Book-Keeping by SINGLE ENTRY chiefly records the transactions on credit, and for this purpose two books are necessary, called the Day-Book, and the Leger. f THE DAY-BOOK. Each page of the Day-Book should be ruled with two columns on the right hand for dollars and cents, and one column on the Best for inserting the page or folio of the Leger on which the account is posted. B R. The Day-Book begins with an account of the owner's property, debts, &c.; then follows a detail of the occurrences of trade, set down in the order of time in which they take place. The name of the person, or customer, is first written with the term Dr. or Cr. annexed, according as he becomes debtor or creditor by the transaction; and this may be distinguished by the following general rule. The person who receives is Debtor, and the person who gives or parts with any thing is Creditor. Thus, if I sell goods on credit, I enter A. B. the buyer, Dr. to the goods, specifying their quantity and value. If I buy goods on credit, I enter C. D. the seller, Cr. by the goods, specifying their quantity and value. By the same rule, if I pay money, the person to whom I pay it, is made Dr. to cash for the amount; and if I receive money, the person from whom I receive it, is made Cr. by cash for the asnOunt. And if debts be contracted or discharged by any other means, the same rule is to be observed; the person who becomes in debted to me, is entered Dr. and the person to whom I become indebted, Cr.—Also, the person whose debt I discharge, is made Dr. and he that discharges a debt due by me, is Cr. Each page of the Leger should be ruled with two columns on the right hand for dollars and cents, and with one column on the left, for entering the date of the transaction. In the Leger, the dispersed accounts of each person in the Day-Book, are collected together, and the Drs. and Crs. are placed upon opposite sides of the same page, or book. N. B. It is usual in commencing business, to mark the first DayBook and Leger with the letter A, and succeeding books, with H, C, &c. * The person's name is written in large characters as a title; on the left hand page, he is styled Dr. and on the opposite, or right hand page Cr.—On these pages the transactions are entered as they stand Drs. or Crs. in the Day-Book. For instance, A. B. is debited for whatever he has bought of me; and on the opposite page, he is credited for the payments he has made. In short whatever I have given him is on the Dr. side, and what he has given me on the Cr. ; and the difference between the Dr. and Cr. sides is called the balance. The Leger should have an index, in which the titles of the accounts should be arran ged under their initial letters, with the number of the page or folio in the Leger, on which the account is posted. * |