MISCELLANEOUS. ed to the same denomination, and add them together for a divisor-the quotient will be the number of times required. 6. In £33 how many guineas, pounds, dollars and shillings, of each an equal number? Ans. 12. 7. A person wishes to draw off a hogshead of wine into gallon bottles, two quart, quart and pint bottles, of each an equal number; how many must he have? Ans. 33 bot. of each kind. and 9pts. over. 8. If 4 men spend, each 14s. 1d. at a tavern, what is the whole bill? Ans. £2. 16s. 4d. 9. What will be the weight of 12 silver cups, each weighing 1lb. 1oz. 20 grains? 10. What will 700 bushels of potatoes cost at 1s. 3d. a bushel? Ans. £43. 15s. 11. How loads, each 18ft.? much wood in 27 containing 1 cord Ans. 30cor. 102ft. 12. If 4 men spend at a tavern £2 16s. 4d. what must each pay? 13. If 12 silver cups weigh 13lb. 1oz. 2pwt. what is the weight of each cup? 14. If 700bu. of potatoes cost £43 15s. what is that a bushel? 15. If 27 loads contain 30 cor. 102ft. of wood, how much in each load? 16. If a person travel 24rd. 12ft. in a minute, how far would he go, at that rate, in 2 hours? 17. If a man drink a pint of | rum a day, how much will he drink in a year? Ans. 45gal. 2qt. 1pt. 18. How many barley corns will reach round the world, supposing it to be 25020 miles? Ans. 4755801600. 19. Divide $120 among 4 men, so that the shares shall be to one another as 1, 2, 3, 4. Ans. 12, 24, 36, 48. 20. How many steps of 2 feet 6 inches, must a man take in going from Burlington to Boston, it being 190 miles? Ans. 401280 steps. 21. If a person travel 12mi. 28rd. in 2 hours, how far does he go in a minute? 22. How many lots, each containing three quarters of an acre, are there in a square mile? Ans. 853 lots, and 40 rods over. 23. If a vintner be desirous to draw off a pipe of wine into bottles containing pints, quarts and 2 quarts, of each an equal number, how many must he have? Ans. 144 of each. 24. There are three fields, one containing 7 acres, another 10 acres, and the other 12 acres and 1 rood; how many shares of 76 rods each are contained in the whole? Ans. 61 shares, and 44 rods over. | 26. In 470 boxes of sugar, each 261b. how many cwt.? Ans. 109cwt. Oqrs. 121b. 27. If cigars cost one and a half cent each, and a person smoke 3 cigars per day, how much will it cost him for cigars during the months of January, February and March, in a common year? Ans. 405 cents, or $4 5cts. 28. What is the difference between six dozen dozen and half a dozen dozen ? Ans. 792. 29. What is the difference between half a solid foot and a solid half foot? Ans. 648 inches. 30. A note was on interest from March 20, 1819, till Jan. 26, 1824; what was the length of time? Ans. 4y. 10mo. 6d. 31. Divide 5 guineas among 8 men-give A. 8d. more than B. and B. 8d. more than C. &c. what does H. receive? Ans. 15s. 2d. H's share. B. 1 69 50 33. M, N, O, and P apprais 25. In 172 moidores at 36s. each, how many eagles, dollarsed a ship as follows, viz. M at and nine-pences, of each an $6700, N at $9000, O at $8750, equal number? and P at $7380; what is the average judgment? Ans. 92 of each, and 68ninepences over, Ans. $7957 50. 34. In 5529600 cubic inches, how many cords of wood? Ans. 25 cords. 35. A and B wishing to swap horses, and disagreeing as to the conditions, referred the matter to three disinterested persons, X, Y, and Z, whose judgments were as follows, viz. X said A should pay B $8, and Y said A should pay B $6; but Z said B should pay A $5; what is the average judgment? Ans. A must pay B $3. A B In the exchange of arX 1.50 $8 ticles, where the judgY 1. 0 6 ment of the referees is Z 1.5 O partly on one side of Ref 3 5 14 B 5 A the equality between 14 them, and partly on the other, subtract one side from the other, and divide the remain3)9(3 Ans. der by the number of referees for the average judgment. 36. C and D wishing to swap farms, referred the subject to O, P, Q and R, and agreed to abide their judgment, which was as follows, viz. O said C should pay D $70; P said C should pay D $100; and Q said C should pay D $55; but R said D should pay C $25; how was the matter settled? Ans. C pays D $50. 37. What is the weight of 4hhd. of sugar, each weighing 7cwt. 3qrs. 19lb.? Ans. 31cwt. 2qrs. 20lb. 38. Three men and 2 boys hoed 30000 hills of corn, and each man hoed two hills while a boy hoed one; how many hills were hoed by each man, and how many by each boy? Ans. Each man hoed 7500, and each boy 3750 hills. 3X2+2=8 Divisor. 39. If $911.555 be divided among 5 men and 4 women, what is each man and woman's share, a man's share being double that of a woman? $65.111=wom's share. Ans. $130.222=man's share. 40. Two places differ in longitude 31°37' 3"; what is their difference in reckoning time, allowing 15° to make an hour? Ans. 2h. 6′ 28′′. REVIEW. 1. When are numbers called compound, or complex? 2. By what are the operations performed by compound numbers regulated? 3. Repeat the table of Federal money, of English money. 4. What are the names and values of the coins of the United States? 5. What are the most common foreign coins? what their several values? 6. What is the table of time? 7. How is the year commonly dis vided? Repeat the number of days in each month. 8. What is meant by leap year? how may we know whether a year is leap year or not? What is meant by old and new style? Let the pupil be questioned in like manner respecting the other tables. Of how 9. What is Reduction? many kinds is it? 10. What is the rule for Reduction Descending? Ascending? 11. What is the method of proof in each? 12. How would you proceed to multiply by 5? to divide by 5? 13. What is meant by Reduction of Decimals? 14. How would you proceed to find the value of a decimal in integers of a lower denomination? How to reduce compound numbers to decimals of a higher denomination? 15. How many days are commonly reckoned to a month, in computing interest? (145) How are days and months reduced to a decimal of a year? 16. What is Compound Addition? -the Rule?-Proof? 17. What is Compound Subtraction?-the Rule?-Proof? 18. If you wish to subtract one date from another, how would you proceed? (152) 19. What is Compound Multiplication?-the Rule? What is Compound Division ?-the Rule? What relation have these two rules to each other? Of what contractions are these rules susceptible? 20. What are the several. contractions of Simple Multiplication? (90, 91, 92, 93,)—of Division? (108, 109, 110, 111.) 21. What is meant by a simple number? What is the distinction between a simple and a compound? 22. How would you proceed to take quantities of several denomi nations, each an equal number of times, from a given quantity? SECTION V. PER CENT. 161. Per Cent. is a contraction of per centum, Latin, signifying by the hundred, and implies that calculations are made by the hundred. Per Annum signifies by the year. 162. Enterest. ANALYSIS. If I lend a neighbor 25 dollars for one year, and he allow me 6 cents for the use of each dollar, or 100 cents, how much must he pay me in the whole at the end of the year? 25 .06 1.50 25. 26.50 If he pay cts. 06 of a dollar (132) for the use of 100 cts. or 1 dollar, he must evidently pay 25 times .06, or (86) .06 times 25-$1.50 for the use of 25 dollars. Hence, 25-1.50 $26.50 is the sum due me at the end of the year. The $25 is called the principal, the .06 is called the rate per cent. the $1.50 is called the interest, and the $26.50 is called the amount. Hence the following DEFINITIONS. 163. Interest is a premium allowed for the use of money. The sun of money upon interest is called the principal. The rate is the per cent. per annum agreed on, or the interest of one dollar for one year, expressed decimally. The principal and interest added together are called the amount. Interest is of two kinds, Simple and Compound. 164. The rate per cent, is expressed in hundredths of a dollar. Decimals in the rate below hundredths are parts of one per cent. The rate of interest is generally established by law. In New-England legal interest is 6 per cent. in New-York 7 per cent. and in England 5 per cent. Where the rate is not mentioned in this work, 6 per cent. is understood. SIMPLE INTEREST. 165. Simple Interest is that which is computed on the principal only. FIRST METHOD. ANALYSIS. 166. 1. What is the interest of $38.12 for 2 years, 8 months and 21 days, at 6 per cent. per annum? $38.12 Multiplying the principal by the rate gives the interest for one year, (161) and the interest for one year multiplied by the number of years, is evidently the in$2.2872 terest for the whole time. Twenty-one days are 3 2.725 of a month=0.7, and 8 mo. 21d.-3.7 mo. But months are 12ths of a year, hence 8.7m.mo. 0.725 year, 114360 (142) and 2yr. 8mo. 21d. 2.725 years, we therefore 45744 multiply 2.2872, the interest for one year, by 2,725, the number of years, and the product, $6.132, is the interest for the whole time. Hence, 150104 45744 $6.1326200 167. To compute the interest on any sum for any time. RULE. Multiply the principal by the rate, expressed as a decimal of a dollar, and the product will be the interest for one year. Multiply the interest thus found by the number of years, (reducing the months and days, if any, to the decimal of a year) (145) and the product properly pointed (106, 116) will be the interest required. NOTE. In solving the following questions, the decimal of a year, when it has not terminated sooner, has been carried to four places of figures, and that will give the interest sufficiently correct for common practice. When great accuracy is required, find the number of days in the given months and days, and divide these by 365, the number of days in a year and the quotient will be the true decimal of a year. |