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1. What difference is there between twice 5 and twenty, and twice twenty-five ?
Ans. 20. 2. In an orchard of fruit trees f of them bear apples, 4 pears, į plums, 60 of them peaches, and 40 cherries ; how many trees does the orchard contain ?
Aps. 1200. 3. A merchant begins the world with $5000, and finds that by his distillery he clears $5000, in 6 years; by his navigation, $5000 in 73 years ; and that he spends in gambling $5000 in 3 years ; how long will bis estate last ?
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. 4 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 min. utes; how many times will they go round themfield before the swifter overtakes the slower !
S A. 161 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 ia 17 minutes. Now, supposing both these to be carelessly left open, and the water to be turned op al 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. 5811 sec. 7. A hare starts 12 rods before a bound; 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; low long will the course hold, and what
will be run over, from the spot where the dog started ?
Ans. 2288 ft. 977 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, add 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 24 ?
Aps. 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, 846 yards ; and from the top of the light house 900 yards ; the height of the light house is required !
Ans. 76.77+ y ds. 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+ miles.
12. If the earth be 7911 miles in diameter, and the moon 2180 iniles ; how many moons will it take to make one earth?
Ans. 47.788 12. A father left his estate of $1300 per annum to his only son, 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?
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 substitutiog part silver was only a proper perquisite, which taking air, Archimedes was appointed to examine it, who op putting it into a vessel of water found it raised the fluid 8.2245 cubick inches, and having discovered that the inch of gold weighed 10.36 ounces, and that of silver but 5.85 ounces, he four:d wbat part of the king's gold had been changed. Repeat the process and inform us what part of it was gold, and what silver ?
28.8038 oz. silver. Ans.
34.1962 oz. gold. 14. A person having driven a stock of cattle to market, received for them all 456 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
C4 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 ; a: the year's end be found that 3150 gigs had passed, and that 7 gigs passed when 5 wagons did, and 4 horsemen passed when 6 tootmen did, and 5 footmen passed when 3 gigs did, what number of wagons, bursemed, and footmen passed, and how much did the gate-keeper receive ?
2250 Ans. Footmen
Amount of toll $353.50 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 ?
Ans. 94m. 7fur. 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 wil, ordered, that, if the child were a son, of his estate should belong to him,
and the remainder to his mother ; but, if it were a daughter, he appointed the mother ş, 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 bad she had only a son ?
Ans. $2100. 18. When first the marriage knot was tied
Betwixt my wife and me,
Aps. 57 and 33. 1) 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 cara ry but two persons at once, and for want of a waterman, they are nes cessitated 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 ?
20. As I was going to St. Ives,
I met seven wives,
How many were going to St. Ives ? 21. À 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 though the corp 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 bundred geese ; says he, I have not an hundred, but if I had half as many as I now have, and two geese and a ball beside the number 1 aow have already, I should bare an bundred. 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 bave 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 ?
(After the scholar, inale or female, has acquired a competent knowledge of Arithmetick, or of its tundamental 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 empluyed 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 inany losses and inconveniences ; to avoid which, the following simple and correet plan is recommended for their adoption.
Let a small book be made, or a few sheets of paper sewed together, and raled 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. 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-Keeping. It contains all the inportant 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 inpressed on the meipory of scholars of common mind, as never to be forgotton ; while their knowledge of common arithmetick and practical 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.
THE DAY-BOOB. 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 left for inserting the page or folio of the Leger on which the accoupt is posted.
The Day-Book begins with an account of the owner's property, debts, &c. ; theu 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 be 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 amount.
And if debts be contracted or discharged by any other means, the same rule is to be observed ; the person who becomes indebted 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.
THE LEGER. 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 he 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 Day-Book and Leger with the letter A, and succeeding books, with B, 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 arranged under their initial letters, with the number of the page or folio in the Leger, on which the account is posted.