21 inches thick, will it take to build a house 44 feet long, 40 feet wide, 20 feet high, and the walls 12 inches thick? 27. What is the value of 87 pigs of lead, each weighing 3 cwt. 2 qrs. 171⁄2 lb., at 8£. 13s. 8d. per fother of 191⁄2 cwt.? 28. What is the tax upon $1153. at $.03 on a dollar? 29. What is the tax upon $843.35, at $.04 on a dollar? 30. What is the tax upon 785£. 11s. 4d. at 2s. 5d. on the pound? 31. Suppose a certain town is to pay a tax of $6145.88, and the whole property of the town is valued at $153647; what is that on a dollar? How much must a man pay, whose property is valued at $23475.67 ? Note. In assessing taxes, the first requisite is to have an inventory of the property, both real and personal, of the whole town or parish, and also of each individual who is to be taxed, and the number of polls. The polls are always stated at a certain rate. Then knowing the whole tax, take out what the polls amount to, and the remainder is to be laid upon the property. Find how much each dollar is to pay, and make a table, containing the portion for 1, 2, 3, &c. to 10 dollars, then for 20, 30, 40, &c. to 100, and then for 200, 300, &c. From this table it will be easy to find the tax upon the property of any individual. 32. A certain town is taxed $3137 43. perty of the town is valued at $89640.76. polls which are taxed $.75 each. lar? The whole proThere are 120 What is the tax on a dolHow much is a man's tax who pays for 3 polls, and whose property is valued at $2507 ? 33. A merchant bought wine for $1.75 per gallon, and sold it for $2.25 per gallon. What per cent. did he gain? 175-25 Note. He gained 50 cents on a gallon, which is of the first cost. It has been already remarked that 1 per cent. is .01, 2 per cent. is .02, &c.; that is, the rate per cent. is always a decimal fraction carried to two places or hundredths. To find the rate per cent. then, first make a common frac tion, and then change it to a decimal .285. Now .28 is 28 per cent. and .0055 is5 per cent. The rate then 2855 ver cent, The two first decimal places taken together being hundredths are so much per cent., and thousandths are so many tenths of one per cent. 10 35 34. A merchant bought a hhd. of molasses for $20, and sold it for $25; what per cent. did he gain? 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. 8d. per gallon, and sold it for 2s. 3d. per gallon. What did he gain per cent? 33. 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£. Ils. 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 in terest ? 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 I£. 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£. 178. 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. ? 47.50 .07 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 5 per cent., and then add of it to itself, or if 5 per cent., subtract; if 72 or 4 per cent. add or subtract 1, &c. Let us take the above example. 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 cen. 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 18th 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 71⁄2 per cent. ? 59. What is the interest of $183 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 8 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. ? 2 66. What is the interest of $.25 for 13 days, at 71 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 per cent.? 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 pcr 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. 1919? 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 One. 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 Two. one are One added to two is called three; two and one are Three. One added three is called four; One added to four is called five; One added to five is called six; One added to six is called seven; six and one are One added to seven is. called eight; seven and one Eight. are three and one are Four. Five. Siz. Seven. One added to eight is called nine; eight and one arc 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 numbers, that are necessary to be used, with very few names. |