42. Bought 175 cords of wood for $437, and sold 93 cords of it at a profit of $1 per cord. At what rate must the remainder be sold to make $974 ou the whole? Ans. $3 per cord.

43. A person who has a journey of 570 miles to perform, proceeds for 9 days at the rate of 333 miles per day. How much must his daily rate be increased or diminished, to complete the journey in 9 more days? Ans. Diminished 33 m.

44. A bought of B 34 yards, and of C 46 yards, of cloth, at $5 per yard. Having sold 4 of these purchases to D, at a profit of $14 per yard, at what rate must the remainder be sold, that his profit may be $150 on the whole? Ans. $7 per yard.

45. What is the Sum of 230 and 3 tenths, 29 and 13 hun dredths, 173 and 5 hundredths, 75 thousandths, and 1350 and 3 ten-thousandths? Ans. 1782.5553.

46. What is the Sum of 625 thousandths, 162 and 5 hundredths, 346 and 9 tenths, 375 thousandths, and 8374 and 15 ten-thousandths? Ans. 8883.9515.

47. What is the Sum of 184 hundredths, 470 and 7 tenths, 951⁄2 thousandths, 436 and 34 tenths, and 4730 and 73 hundredthousandths? (§ 144.) Ans. 5637.30873.

48. What is the Product of 375 and 125 thousandths, multiplied by the difference between 75 hundredths and 31 thousandths? Ans. 269.714875.

49. What is the Product of 43 and 74 ten-thousandths, multiplied by the difference between 5 hundred-thousandths and 31 hundredths? Ans. 1.503108630.

50. What is the Product of 25 millionths multiplied by the sum of 300 and 5 tenths, 17 thousandths, and 10 and 64 tenths? Ans. .00777855.

51. What is the Quotient of 384 and 19 hundredths, divided by the sum of 9 thousandths, 6 hundredths, 2 tenths, and 3 and 5 tenths? Ans. 101.934'.

52. What is the Quotient of 7340 and 16 hundred-thousandths, divided by the difference between 6357 and 8 tenths, and 736 and 34 hundredths? Ans. 1.305'.

53. What is the Quotient of 803 and 154 hundred thousandths, divided by the difference between 25 hundred-thousandths, and 24564 and 625 ten-thousandths? Ans. .0326'.

54. Find the sum that should be paid for 3 cords of wood at $2.18 per cord, 10 bushels of apples at 871 cents a bushel, and 125 pounds of beef at 64 cents a pound.

In these Exercises, reduce Vulgar Fractions to Decimals. Ans. $24.21875. cents per yard, for enough of calico at How much calico must Ans. 181.25 yd.

55. A gives B 117 yards of silk at 93

20 yards of cloth at $4.37 per yard, and
12 cents per yard to pay the balance.
A receive?

56. How much rice at 4 cents a pound, would be an equivalent for 100 pounds of coffee at 12 cents a pound, 300 pounds of sugar at 7 cents a pound, and 25 pounds of tea at $1 a pound? Ans. 1305.555' lb. 57. A miller sold 75 barrels of flour at $4.87 a barrel, and with the proceeds intends to purchase, in equal quantities, wheat at 75 cents a bushel, rye at 314 cents a bushel, and corn at 371 cents a bushel. What quantity of each can he purchase?

Ans. 254.347' bushels.

58. A gives B 37 cut. of hemp at $4.333 per cwt., for 1000 pounds of bacon at 64 per pound, $20 in cash, and as much sugar at 74 cents per pound as will pay the balance. What quantity of sugar must A receive? Ans. 1073.393' lb.

59. A merchant bought 100 yards of cloth at $3.933 per yard, and 821 yards at $4.121 per yard. At what average price per yard should he sell the whole, to realize a profit which shall be equal to of the cost? $Ans. 5.027'.

60. A speculator bought 210 barrels of flour at $4 a barrel, 965 bushels of oats at 33 cents a bushel, and 50 barrels of pork at $5.064 a barrel. He sold the flour and pork at an advance of $2.5 a barrel, and the oats at a loss of 3 cents a bushel: what was the result of the speculation?

Ans. He gained $621.03'. ·

II.

OPERATIONS ON MONOMIALS AND POLYNOMIALS.-CURRENCIES.DUODECIMALS.-ALIQUOT PARTS.

61. A jeweler sold 3 lb. 9 oz. 15 dwt. 18 gr. of silver plate, at $2.25 per oz. What did the whole amount to?

The pupil should be required to explain the different methods of solving questions of this kind. (§ 178, § 209.)

Ans. $103.02'.

62. A farmer sold 3 T. 16 cwt. 3 qr. 21 lb. of hemp, at $5 per cut., and invested the proceeds in land at $37 per acre. How much land did he purchase? Ans. 10 A. 1 R. 1.28' P.

63. A grocer exchanged 29 gal. 3 qt. 1 pt. of brandy, at 434 cents per gallon, for rye at 314 cents per bushel. What quantity of rye did he thus obtain ? Ans. 41 bu. 3 pk. 2 qt. .8 pt.

64. A brewer bartered ale at 37 cents per gallon, for 25 bu. 2 pk. 1 qt. of barley at 40 cents per bushel. ale was thus disposed of?

What quantity of Ans. 27 gal. 1.864' pt.

65. A laborer dug 130 rd. 4 yd. 21 ft. of ditching, at $2.5 per rod, for which he took $100 in cash, and wheat at 87 cents a bushel. How much wheat did he get?

Ans. 259 bu. 2 pk. 4 qt. 1.66' pt.

66. Find the sum that should be paid for 3 T. 21 cưt. and 34 qr. of hemp, at $41 per cwt. Ans. $284.904'.

67. A townsman who had a lot of ground containing 54 A., sold to each of two persons 3 R., at the rate of $100 per acre. What is the remainder of it worth at the same rate?

Ans. $350.

68. A merchant sold some remnants of cloth, containing 31 yd., 24 yd., 34 gr., and 11 gr., at the rate of $3 per yard. What did the whole amount to? Ans. 20.436'.

69. A person who had a journey of 735 miles 5 fur. to perform, went 13 days at the rate of 40 m. 3 fur. 20 p., and 2 days at the rate of 39 miles per day. What distance then remained to be traveled? Ans. 130 m. 7 fur. 20 p.

70. A bought a tract of land containing 570 A. 3 R.; of which he sold to one person 90 A. 1 R. 20 P., and three times that quantity to another, at $273 per acre. What is of the remainder of the tract worth, at the same rate? Ans. $3813.

71. At the rate of 1 bu. 3 pk. per acre, how much ground could be sowed with 35 bu. 2 pk. 5 qt. of wheat? Ans. 20 A. 1 R. 20 P.

72. If 45 yd. 2 qr. of carpeting be required to cover the floor of a room, what part of the floor may be covered with 13 yd. 3 qr. of the same? Ans. .304'.

73. A bought of B 42 T. 13 cwt. 2 gr. of iron, of which he sold 18 T. 14 cwt. to C, and the remainder to D. What part of the whole quantity did he sell to each?

Ans. .438' to C; .561' to D.

74. What should be paid for plastering one side of a wall which is 30 ft. 10 in. long, and 8 ft. 9 in. high, at 183 cents per square yard? Ans. $5.620'.

75. How many square yards of paper would be required to cover the walls of a room which is 10 ft. 6 in. high, and 56 ft. in compass,—deducting for doors, windows, &c.?

12

Ans. 59 s. yd. 8 s. ft.

76. The invoice of a lot of broadcloth imported from Liverpool, amounted to 125£ 16s. 10d. sterling. Required the amount in Federal Money, according to the legal value of the pound sterling in the United States. Ans. $609.070'.

77. What would be the cost of excavating a cellar 36 ft. long, 25 ft. 8 in. wide, and 8 ft. 10 in. deep, at $1.06

per cubic yard? Ans. $321.189'.

78. A Southern merchant purchased in New-York, 95 ya. 3 qr. of calico at 1s. 6d. per yard, 39 yd of cloth at 20s. per yard, and 45 yd. 2 gr. of silk at 8s. 6d. per yard. What was the amount of his bill in Federal Money? Ans. $165.179'.

79. A reservoir for water is 10 ft. 3 in. in length, 8 ft. in breadth, and 4 ft. 11 in. in depth. How many barrels of water will it contain? Ans: 68 bur. 22 gal. 1 qt. 1.712' pt.

80. A farmer wishes to construct a crib which shall contain 1000 bushels. What must be the length of the crib, allowing its height to be 7 ft., and its breadth 9 ft. 6 in.?

с

Ans. 18.713' ft.

III.

RATIO.-PROPORTION.-ANALYSIS.

81. Find the fourth proportional to 3, 5, and 7 cwt. 3 qr., that is, the quantity to which 7 cwt. 3 qr. has the same ratio that 3 has to 5. Ans. 12 cwt. 3 qr. 18.592' lb.

82. Find the inverse fourth proportional to 5, 13, and 2 T. 10 cwt. 20 lb., that is, the quantity to which 2 T. 10 cut. 20 lb. has the inverse ratio 5 to 13, Ans. 19 cwt. 1 gr. 3.36' lb. 83. Find the direct and also the inverse fourth proportional to 15 bu. 3 pk., 25 bu. 2 pk. 5 qt., and 3£ 12s. 8d

Ans. 5£ 18s. 4.08'd.; and 2£ 4s. 7.2'd.

84. If 12 could accomplish a certain work in 91 days, in what time ought 17 men to do the same work?

In these Exercises the pupil should be required to state, in general terms, the kind of proportion involved in the question. Thus, The time required is inversely as the number of men, (§ 220). Ans. 6 days.

85. If .75 T. of iron cost $371, what should be paid for 18 cwt. 3 qr. 10 lb. of iron at the same rate?

The pupil should also be required to give verbal, analytical solutions of these questions. The Analysis of the present one might be as follows:

$371⁄2 divided by .75 is the value of 1 ton; and the value of one ton multiplied by 18 cut. 3 qr. 10 lb., reduced to the denomination of ton, is the value of 18 cwt. 3 qr. 10 lb.

Ans. $47.05'. 86. If 5 acres of ground produce 170 bu. 6 qt. of wheat, how many bushels would 37 A. 2 R. 16 P. 20 s. yd. produce at the same rate? Ans. 1163 bu. 2 pk. 2.656' qt.

87. Allowing a mechanic to earn $62.871 in a month, by working 94 hours per day, what ought he to earn in a month by working 11 hr. per day? Ans. $78.168'.

88. If $20 will supply a family with flour at $5 a barrel, for 3 months, how long would the same sum supply them with flour at $4 a barrel? Ans. 3 months.

$27.87?

89. What should be paid for 17 yd. 2 gr. of cloth, if 4 yd. 3 gr. of the same selts 10 Ans, $100.064'. 90. A company of emigrants has a supply of bread for 25 days, at an allowance of 14 lb. to each per day. How long would the supply last them at an allowance of 12 oz. per day? Ans. 413 days.

91. A lot of ground which is 40 p. 2 yd. long, and 27 p. wide, is equivalent in area to another which is 531 p. long.. What is the breadth of the latter? Ans. 20.37' p.

92. Three pipes of equal size will fill a cistern with water in 13 hr. 40 m. In what time would 5 such pipes fill a cistern whose capacity is 23 times that of the first one?

Ans. 20 hours.

93. If A could build a wall in 3 days, B in 5 days, and C in 6 days, in what time could the three together build the wall? In this question, as well as those which immediately follow, the proportion involved is not very apparent, so that the analy tical will probably be found the most obvious method of solution. Ans. 13 days.