43. Reduce $203 to guineas, (England.) See Table.

A. 40.

A. 3523.

44. Reduce 40 guineas to American eagles, (new.) A. 20E. $3. 45. Reduce 450 sovereigns to Federal money. A. $2,183.123. 46. Reduce 100 shilling pieces, (England,) to dollars. A. $22. 47. Reduce 40 double louis (old) to English crowns. 48. Reduce 80 Napoleons to American eagles. A. 30E. $8.08cts. 49. Reduce 100 Spanish coronilla to sovereigns. A. 20S. 5s. 8d. 50. Reduce 17,000 johannes, (Port.) to Napoleons, A. 75,327.+ 51. Reduce 2,523 gold Lions, (Belgium,) to $. A. $12,731.058. 52. Reduce 1,333 ducats, (new, Russia,) to $. A. $3,063.049 53. Reduce 8,042 Chr. d'ors to ducats, (Sicily.) A. 40,421+. 54. Reduce 10,668 duc. (Cologne,) to pistoles, (Bk.) A. 6,255318 55. Reduce 3,500 silver rupees, (Madras, E. Indies,) to Carolins, (Bavaria.) A. 317 nearly.

A. $2,000.7777.

56. How many dollars, in Federal money, will pay a debt of £450 3s. 6d. in Great Britain? 57. How many reals plate, in Spain, may be purchased for £234 sterling? A. 10,400 reals plate.

58. In cases like the last, either proceed as in the Rule of Three, or first reduce to Federal money.

59. How many rix dollars, (Prussia,) will discharge a debt of 1800 francs, (France ?) A. 489 rix dollars. 60. A bought 400 yards of silk, in Paris, at 3 francs per yard. What was its cost in Federal money? A. $223.20.

61. How many rigsbank dollars, (Denmark,) will purchase 1,575 liras in Genoa? A. 468212

62. How many American dollars will cancel a debt of 7,400, tales in China? A. $10,952. 63. United States on England, (cxv. 31.) Reduce £840. 14s. 6d. sterling, to Federal money, exchange at 3 per cent. advance.

A. $3,848.6522. 64. Great Britain on the United States. What sum, in London, will purchase a Bill on Boston for $8,967.75, exchange at 4 per ct discount? A. £1937. 8d. +

65. What sum in American eagles, (old,) will purchase 4,500 guineas, at a premium of 3 per ct.? (cxv. 33.) A. 2,027E. $5.59.+ 66. United States on France. Reduce 1,174 francs 60 centimes to Federal money, exchange at 5 francs 40 centimes per dollar. A. $217.519 nearly.

67. France on the United States. Reduce $15,000,000, the cost of the Louisiana territory, to the currency of France, exchange at 5 francs 39 centimes per dollar. A. 80,850,000 francs.

68. United States on Amsterdam. Reduce 1,250 florins to Federal money, exchange 39 cents per florin.

A. $487.50.

69. Russia on the United States. Reduce 240 rubles 5 grieveners to Federal money. Exchange at par.

A. $180.37.

70. United States on Denmark. Reduce 424 rigsbank dollars to Federal money, exchange at 2 per cent. in favor of Denmark. A. $229.214.

71. A merchant in Boston bought in London 40 pieces of black broadcloth, each containing 294 yards, for 13s. 6d. per yard. How many eagles (new) at a premium of 2 per cent., must he remit to settle the bill? A. 350 eagles.

72. If you purchase in China, 20,000lb. of tea, for 2 maces per lb. which you sell in Amsterdam for 1 guilder per pound, worth in the United States 2 per cent. advance, and with the proceeds purchase a bill on New York at 5 per cent. discount, what will be your profit in the whole transaction? A. $2,669.47313.

MISCELLANEOUS EXAMPLES.

CXVII. 1. Suppose you employ a capital of $3,000, and invest 315 dollars 9 cents in cloths, 176 dollars 6 cents in linens, 3 times the last amount in silks, 518 dollars 8 dimes 5 mills in various other foreign articles, and the balance in domestic cottons at 12 cents per yd.; how many yds. could you purchase? A. 10,990yd. 2qr. 11⁄2na.

2. Suppose a person at Boston, and another at Philadelphia, the distance between each place being about 300 miles, set out to meet each other on the road. Required how far they are distant when each has traveled 79m. 5fur. 200 yd.? A. 140m. 4fur. 7rd. 1 yd.

3. The sum of £1,261 was left a person in the United States, by a relative in England, to be divided between a mother, son, and daughter, so that the son shall have three times as much as his mother, and the mother double that of the daughter; required the share of each.

A. The daughter's, £140; the mother's, £2803; the son's, £8403. 4. A tract of land measuring 7,495A. 3R. 32rd. is to be divided among a regiment consisting of a colonel, a major, 5 captains, 9 lieutenants, 6 ensigns, 20 sergeants, and 450 privates, so that a sergeant is to have twice as much as a private, an ensign 8 shares, a lieutenant 12, a captain 20, the major 30, and the colonel 50; required the share of each, and the value of the land at 3 dollars per acre?

=

Answers.-Soldiers, 9A. 12rd.= $27.22; sergeants, 18A. 24rd. $54.45; ensigns, 72A. 2R. 16rd = $217.80; lieutenants, 108A. 3R. 24rd.= $326.70; captains, 181A. 2R.= $544.50; major, 272A. 1R. $816.75; colonel, 453A. 3R.= $1,361.25.

5. Jacob, by contract, was to serve Laban, for his two daughters, 14 years; when he had accomplished 10Y. 10mo. 10wk. 10da. 10h. 10m., how many minutes had he then to serve ? A. 1,416,350.

6. Suppose you were 15 years old on the first day of January, 1810, how many seconds old must you have been on the first day of August, 1840, making due calculations for the leap years and the days in each month from one date to the other? A. 1,438,473,600 seconds.

7. How much time has elapsed from Nov. 19th, 1826, to Jan. 15th, 1830; from April 19th, 1815, to Sept. 20th, 1837; and from June 12th, 1836, to March 1st, 1839 ?

A. 3y. 1m. 26d.; 22y. 5m. 1d.; 2y. 8m. 19d.

8. How many barrels can be filled with 60 hogsheads of molasses, each containing 62 gallons, 3 quarts, 1 pint, 3 gills? A. 1197 bl.

9. A vintner bought 138 gallons of wine, at 10s. a gallon, of which he retained 18 gallons for his own use; at what rate must he sell the remainder, that he may have his own for nothing? A. $1.913.

10. The national debt of England, some time ago, amounted to 820 millions sterling.

sum.

11. Required the number of shillings and guineas (21s.) in that A. 16,400,000,000s.; 780,952,381 guineas. + 12. Required the weight of the debt in guineas, (gold,) each weighing 5dwt. 9gr. A. 17,490,079lb. 4oz. 7dwt. 21gr. 13. Required the weight of the debt in shilling pieces, (silver,) each weighing 3dwt. 21gr. A. 264,791,6663lb. 14. Required the weight in one pound notes, (£1,) 120 weighing 1 A. 213T. 10cwt. 3qr. 8lb. 5 oz.

ounce.

15. Required the time it would take a person, allowing him to count 100 pieces or notes in a minute for 10 hours of the day, (Sundays excepted,)—

To count the debt in guineas. A. 41Y. 182da. 8h. 44m. nearly. To count the debt in shillings.

To count the debt in notes, (£1.)

A. 873Y. 84da. 3h. 20m.

A. 43Y. 207da. 6h. 40m.

16. Required how many wagons, loaded with 1,200lb. each, would

17. Required the number of miles the wagons would extend, allow

ing 30 feet to each wagon and horses

When they are loaded with shillings.
When they are loaded with guineas.

When they are loaded with pound notes.

A. 1,253m. 6fur.

A. 82m. 6 fur. A. 2m. 7rd. 14yd.

18. Required the yearly interest of the debt. A. $218,666,666.663. 19. Required the number of years that would be required to pay off the debt by an annual assessment of 9 pence per pound on the value of the whole property in Britain, which, according to the estimate of Dr. Colquhoun, is £2,736,640,000. A. Almost years.

20. Required what per cent. and what sum on the pound the British proprietors must assess themselves, supposing that, by a generous exertion, they agree to pay off the debt at once.

A. 30 per cent. nearly. 21. What is the greatest common divisor of 204, 1,190, 1,445, and 2,006?

A. 17.

22. Find the greatest common measure of 63 and 168, with which divide their sum, difference, and common multiple. A. 21. 23. Hence, if any number will measure each of two others, it will measure their sum, their difference, and their common multiple.

24. Since the common measure of two or more numbers becomes, when those numbers are multiplied together, or when each is multiplied into itself, a factor in every product, therefore

25. A common measure of two or more numbers will measure the squares, cubes, &c. of those numbers, also the continued product of those same numbers into each other.

26. What is the least common multiple of 2, 3, 4, 6, 7, 12, and 14?

151. 602

A. 84. 27. Reduce 24, 5, 127, and 54, to their equivalent improper fractions. A. ; ; 12; 17. 28. Reduce to improper fractions 417, 123, 27513, and 374,543. A. 540; 2095; 4132; 28876. 103 29. Reduce to mixed numbers 135 of 7, of of 121, and 15,7 of 8 of 133. A. 99; 4; 1,8477.

103

21

30. Reduce

33

to a simple fraction.

A. 99 145.

133

31. Reduce to mixed numbers 8357. 18793 of 4 of 63; of 278 359

8398

29

47

A. 30; 521; 1; 278.

11050

32. Reduce to prime terms 9395; 35581; 10000000; 222210

33. Find the least common denominator of,,,, and .

34. Find the least common denominator of 21, 4 of 93, and

36. What is the difference between of and of 15-between

37 How many times is the sum of 5 and 3 greater than their difference?

38. Multiply together 2 39. Find the continued product of 324, 18, 21, and 21. A. 1.

361

1444 441

40. Find the value of 3 of 4 of 34+5 of 33.

41. Express of a yard as the fraction of an inch, and 14 of an

42. Required the sum and difference of of a pound, and ‡ of a guinea, (21s.) A. £1. 2s. 8d.; 4s. 43. Reduce of a pound, 22 of a guinea, and of 3s. 91d. to fractions of the same denomination, and to the same denominator. 7056 7007

7040 A.

· 1392

44. The aggregate of 3 of 3 of a sum of money is $133; what is that sum ? A. $332 45. Find the fraction which, when multiplied by 3 of 4 of 31, gives a result equal to 7. A. 12. 46. A person having of a coal mine, sells of his share for $2,000; what is the whole mine worth? A. $6,666.663. 47. The third part of an army was killed, the fourth part taken prisoners, and 1,000 fled. How many were there in the army? how many killed?-how many taken prisoners?

A. 2,400; 800 killed; 600 prisoners.

48. A can do a job of work in 5 days, B in 6, and C in 7; how much can they jointly do in 2 days? A. 18 job. 49. The owner of of a ship sold of of his share for $1233; 211 what would

of cost at the same rate?

A. $200.

50. If a cask be emptied by two taps in 4 and 6 hours respectively, in what time will it be emptied by both of them together, the rates of efflux remaining the same throughout? A. 2h. 24m.

51. A, B and C can perform a piece of work in 12 hours; also, A and B can do it in 16 hours, and A and C in 18 hours; what part of the work can B and C do in 94 hours, and in what time would A do the whole ? A. 28h. 48m. 52. What decimal fractions are equivalent to 5, 125, and 20? A. .16; .072; .006640625.

4

:

ก

A. .876,543,211.

53. From unity take .123456789.
54. Find the continued product of .275, 2.75, and 27.5.

A. 20.796875.

55. Find the sum of the quotients of 1.68 by .024, of 971.7 by 123, and of 142.025 by .0437, and prove the results by vulgar fractions. A. 3,327.9.

56. One man owns .6 of a bank, another, and Mr. Darby the rest; what is Darby's part, and what the value of each part, allowing the capital of the bank to be $100,000?

A. $27,500; $60,000; $12,500.

57. In a certain school, .125 of the pupils study geography, .3 study grammar, arithmetic, and 18 learn to read. What is the number in each branch? A. Geography, 30; grammar, 72; arithmetic, 120; reading, 18. Whole number, 240.

58. A man whose annual income is $3,000, spends .12 of it; how many dollars will he have saved at the end of each year?

A. $2,640.