MISCELLANEOUS. 159. 1. How many seconds | ed to the same denomination, 28 years of 365d. 6h. each? Ans. 883612800. 2. How many seconds from the birth of Christ to the end of the year 1824, allowing 365d. 5h. 48m. 57s. to a year? Ans. 57559853088. 3. How many seconds in 8s. 12° 14′ 26"? Ans, 908066. 4. How many inches from Montpelier to Burlington, it being 38 miles? Ans. 2407680. 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 numAns. 12. ber? 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 bottles 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. 1pwt. 20 grains? 10. What will 700 bushels of potatoes cost, at 1s. 3d. a bushel? Ans. £43 15s. 11. How much wood in 27 loads, each containing 1 cord 18ft.? 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. loz. 2pwt., what is the weight of each cup? 14. If 700bu. of potatoes cost £43 15s, what is that a bush el? 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. 25. In 172 moidores at 36s. each, how many eagles, dollars and nine-pences, of each an equal number? Ans. 92 of each, and 68 nine-pences over. 26. In 470 boxes of sugar, each 26lb., how many cwt.? Ans. 109cwt. Oqrs. 12lb. 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 5 cts. 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. 4yr. 10mo. 6d. 31. Divide £7 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. 32. A horse is valued by A at $60, by B at $69 50, and by Cat $72 25; what is the average judgment? 34. In 5529600 cubic inches, | should pay D $100; and Q how many cords of wood? said C. should pay D $55; but R said D should pay C $25; how was the matter settled? 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. In the exchange of A B articles, where the X1 $0 $8 judgment of the ref 6 Y10 Z150 erees is partly on one side of the equalRef. 3 5 14 ity between them, and partly on the other, subtract one side from the other, 14 B 3)9(3 Ans. and divide the remainder by the number of referees for the average judg ment. 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 Ans. C pays D $50. 37. What is the weight of 4hhd. of sugar, each weighing 7cwt. 3qrs. 191b. Ans. 31 cwt. 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. 3×2+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? 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. 7. How is the year commonly divided? 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 to hles. 4. What are the names and valnes 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 ? 9. What is Reduction ? Of how many kinds is it? 10. What is the rule for Reatio¡tion Descending? Ascending! 11. What is the method of proof fu 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 denominations, 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. Interest. ANALYSIS. 162. 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. If he pay 6 cents.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 rute per cent., the $1.50 is called the interest, and the $26.50 is 26.50 called the amount. Hence the following DEFINITIONS. 163. Interest is a premium allowed for the use of money. The sum 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 prineipal 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. $2.2872 114360 160 104 $6.2326200 Multiplying the principal by the rate gives the interest for one year, (162) and the interest for one year multiplied by the number of years, is evidently the interest for the whole time. Twenty-one days are of a month=0.7, and 8 mo. 21d. 8.7 mo. But months are 12ths of a year, hence 8.7m. mo. 0.725 year (142), and 2yr. 8mo. 21d.2.15 years; we therefore multiply 2.2872, the interest for one year, by 2.725, the number of years, and the product, $ 6.232, is the interest for the whole time. Hence, 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 * 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. |