35. A merchant bought a quantity of flour for $137, and sold it for $143; what per cent. did he gain?

36. A man bought a quantity of goods for $94.37, and sold them for $83.92. What did he lose per cent.?

37. A merchant bought molasses for Is. Sd. per gallon, and sold it for 2s. 3d. per gallon. What did he gain per cent? 38. A merchant bought wine for 11s. 3d. per gallon, and sold it for 9s. 8d. What per cent. did he lose?

39. A merchant bought a quantity of goods for 37£. 15s Ed.; and sold them again for 43£. 11s. 4d. What per cent

did he gain?

40. A man buys a quantity of goods for $843; what per cent. profit must he make in order to gain $157 ?

41. A man failing in trade owes $19137.43, and his property is valued at $13472.19. What per cent. can he pay? 42. A man purchased a quantity of goods, the price of which was $57, but a discount being made, he paid $45.60. What per cent. was the discount?

43. A man hired $87 for 1 year, and then paid for principal and interest $92.22. What was the rate of the interest?

44. A man paid $12.81 interest for $183, for 2 years. What was the rate per year?

45. A man paid $13.125 interest for $135, for 1 year and 6 months. What was the rate per year?

46. A man paid $4.37 interest for $58, for 1 year and 8 months. What was the rate per year?

47. 4s. 6d. sterling of England is equal to 1 dollar in the United States. What is the value of 1. sterling in Federal

money

?

48. How many dollars in 35£. sterling?

49. How many dollars in 27£. 14s. 8d. ?

Note. Change the shillings and pence to the decimal of a pound, by the short method shown above. 50. How many dollars in 187£. 17s. 4d.? 51. In $19.42 how many pounds sterling? 52. In $157 how many pounds?

53. In $2384.72 how many pounds?

54. Bought goods in England to the amount of 123€. 17s. 9d.; expenses for getting on board 3£. 5s. 8d.; $8.50 freight; duties in Boston 15 per cent. on the invoice; other expenses in Boston $15.75. How many dollars did the goods cost? How much must they be sold for to gain 12 per cent. on the cost?

55. What is the interest of $47,50 for 1 year, 7 months, and 13 days, at 7 per cent.?

I first find the interest for 1 year, and then of that is the interest for 6 months; of the interest for 6 months will be the interest for 1 month; of the interest for 1 month will be the interest for 10 days, and of the interest for 10 days. is very near the interest for 3 days. All these added together will give the interest for the whole time. In a similar manner, the interest for any time at any rate per cent. may be calculated.

When there are months and days, it is better to calculate the interest first at 6 or 12 per cent., and then change it to the rate required. Observe that 1 per cent. is of 6 per cent., 1 per cent. is of 6 per cent., 2 per cent is of 6 per cent, &c. Hence if the rate is 7 per cent., calculate first at 6 per cent., and then add of it to itself, or if 5 cent., subtract; if 71 or 4 per cent. add or subtract 4, &c. Let us take the above example.

16

per

6 per cent. for 1 year, 7 months, and 13 days, is 97% per cent. nearly, that is .097.

47.50

.097

33250

42750

of 4.60750 Interest at 6 per cent.

7679 do. at 1 per cent.

$5.3754

This answer agrees with the other within about 1 cent. Greater accuracy might be attained, by carrying the rate to one or two more decimal places.

56. What is the interest of $135.16 from the 4th June, 1817 to 13th April, 1818, at 5 per cent. ?

57. What is the interest of $85.37 from 13th July, 1815, to 17th Nov. 1818, at 4 per cent. ?

58. What is the interest of $45.87 from 19th Sept. 1819, to 11th Aug. 1821, at 71 per cent. ?

59. What is the interest of $133 from 23d Oct. 1817, to 19th Jan. 1820, at 4 per cent. ?

60. What is the interest of 113£. 14s. for 1 year, 5 months, and 3 days, at 7 per cent. ?

61. What is the interest of 87£. 15s. 4d. for 2 years, 11 months, 3 days, at 7 per cent. ?

62. What is the interest of 43£. 16s, for 9 months and 13 days, at 8 per cent. ?

63. What is the interest of 142£. 19s. for 1 year, 8 months, and 13 days, at 9 per cent. ?

64. What is the interest of $372 for 4 years, 8 months, and 17 days, at 74 per cent. ?

65. What is the interest of 1 dollar for 15 days at 7 per cent.?

66. What is the interest of $.25 for 13 days, at 7 per cent.? 67. What is the interest of $.375 for 19 days, at 11 per cent. ?

68. What is the interest of $1147 for 8 hours, at 6 cent.?

per

69. What is the interest of 137£. 11s. for 11 days at 9 per cent. ?

70. What is the interest of 15s. for 3 months, at 8 per cent. ?

71. What is the interest of 16£. 7s. 8d. for 2 months, at 12 per cent.?

72. What is the interest of 4s. 3d. for 17 years, 3 months, and 7 days, at 8 per cent. ?

73. A man gave a note 13th Feb. 1817, for $753, interest at 6 per cent., and paid on it as follows: 19th. Aug. 1817, $45; 27th June, 1818, $143; 19th Dec. 1818, $25; 11th May 1819, $100; and 14th Sept. 1820, he paid the rest, principal and interest. How much was the last payment?

74. A note was given 17th July, 1814, for $1432, interest at 6 per cent., and payments were made as follows; 15th Sept. same year, $150; 2d Jan. 1815, $129; 16th. Nov 1815, $23; 11th April, 1817, $237; 15th Aug. 1818, $47. How much was due on the note, principal and interest, 5th Feb. 1819?

ARITHMETIC.

PART II.

NUMERATION.

I. A single thing of any kind is called a unit or unity.
Particular names are given to the different collections of

units.

A single unit is called

Onc.

If to one unit we join one unit more, the collection is called two; that is, one added to one is called two, or one and

one are

are

Four.

Five.

Six.

Two. One added to two is called three; two and one are Three. One added three is called four; three and one are One added to four is called five; four and one are One added to five is called six; five and one are One added to six is called seven; six and one are Seven. One added to seven is called cight; seven and one Eight. One added to eight is called nine; eight and one are Nine. One added to nine is called ten; nine and one are Ten. In this manner we might continue to add units, and to give a name to each different collection. But it is easy to perceive that, if it were continued to a great extent, it would be absolutely impossible to remember the different names; and it would also be impossible to perform operations on large numbers. Besides, we must necessarily stop somewhere; and at whatever number we stop, it would still be possible to add more; and should we ever have occasion to do so, we should be obliged to invent new names for them, and to explain them to others. To avoid these inconveniences, a method has been contrived to express all the num→ bers, that are necessary to be used, with very few names.

The first ten numbers have each a distinct name. The collection of ten simple units is then considered a unit: it is called a unit of the second order. We speak of the collections of ten, in the same manner that we speak of simple units; thus we say one ten, two tens, three tens, four tens, five tens, six tens, seven tens, eight tens, nine tens. These expressions are usually contracted; and instead of them we say ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety.

The numbers between the tens are expressed by adding the numbers below ten to the tens. One added to ten is called ten and one; two added to ten is called ten and two; three added to ten is called ten and three, &c. These are contracted in common language; instead of saying ten and three, ten and four, &c., we say thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen. These names seem to have been formed from three and ten, four and ten, &c. rather than from ten and three, ten and four, &c., the number which is added to ten being expressed first. The signification, however, is the same. The names eleven and twelve, seem not to have been derived from one and ten, two and ten; although twelve seems to bear some analogy to two. The names oneteen, twoteen, would have been more expressive; and perhaps all the numbers from ten to twenty would be better expressed by saying ten one, ten two, ten three, &c.

The numbers between twenty and thirty, and between thirty and forty, &c. are expressed by adding the numbers below ten to these numbers; thus one added to twenty is called twenty-one, two added to twenty is called twenty-two, &c.; one added to thirty is called thirty-one, two added to thirty is called thirty-two, &c.; and in the same manner forty-one, forty-two, fifty-one, fifty-two, &c. All the numbers are expressed in this way as far as ninety-nine, that is nine tens and nine units.

If one be added to ninety-nine, we have ten tens. We then put the ten tens together as we did the ten units, and this collection we call a unit of the third order, and give it a It is called one hundred.

name.

We say one hundred, two hundreds, &c. to nine hundreds, in the same manner, as we say one, two, three, &c.

The numbers between the hundreds are expressed by adding tens and units. With units, tens, and hundreds we