much more profitable is the making of cheese than butter, the price of butter being 25 cts. per pound, and that of cheese 8 ets. per pound? A. $110,40. 44. If a field will feed 10 cows four weeks, how long will it feed 40 cows? A. 1 week. 45. A man bought a cask of wine, containing 126 gallons, for $15, and sold it at the rate of $2,75 per gallon; how much was nis whole gain? how much per gallon? and how much per cent.? A. His whole gain, $31,50; per gallon, $,25; then, 2501 per cent. 2.50 46. The rent of a certain farm is $500; the tenant employs 2 men; to each he pays $11 a month for 8 months-184; also a boy by the year, who is to have 2 suits of clothes, each worth $8,75-1750, besides his board, while attending school, 3 months, or 12 weeks of the year, which is worth $,93 per week-1116; in the course of the year, the tenant loses 40 good merino sheep, valued at $5 per head-200; the skins brought him $1,12 apiece-45; the other expenses of the year are calculated to average about $,39 per day-14235; the sales of the farm are as follows, viz: 1000 bushels of Potatoes, .... at $0,42 per bushel,-420, Turnips, 400 pounds.. Merino Wool,. 56, 14850, .... 276, 15903, . pound, 575, 3360, 1750, $0,45.. pound, 180, 90, quart, 8, and 20 calves, at $44 per head-90; he carries 70 barrels of or der to the distillery, for one half of which he is to receive 1 qt. of cider-brandy for 4 qts. of cider; the rest brings him $1,13 per barrel-3955; how much cider-brandy will he receive? and how much will he clear, after deducting all the expenses of managing the farm, including the rent and loss, froni the total amount of sales? A $1338,57; 11024 qts. cider-brandy. 47. What difference is there between the compound interest of $10000 for 8 years, and the simple interest of the same sum for the same time? 4. $1138,48. 48. What is the difference between the compound interest of $500 for 4 years, and the discount of the saine sum for the same time? Å. $34,463. 49. What is the difference between the amount of $1800, at compound interest, for 3 years, and the present worth of the same sum for the same time? A. $618,405. follows: his services for the two last years, at $26 per month turned in a note on James Spencer, of 500 dollars, with 5 years' compound interest due on it-669112; and, for the balance, he was to give his note, payable in 6 years from the date of the transaction, without interest: now the question is, what sum of ready money will discharge said note? A. $93,557. After the clerk had purchased the above stock, and settled for the same, he commenced business for himself. The rent of his store costs him $29 a year; his clerk-hire $27,814 precisely, in addition to which is the interest of his capital, $1420,35, (that is, the interest of the amount of stock, after the 15 per cent. is deducted, $85221). He next considered what price he must put on each article, to make a certain per cent He recollected that the goods were already rated in the inven tory at 15 per cent. more than their actual cost. Now, said he, if I can make 5 per cent. in advance on their present valua tion, clear of all expenses, I shall be satisfied. The question, then, is, at what price he must mark each article, commencing with the first on the inventory, so as to clear the 5 per cent. The pupil will find, by calculation, that the expenses amount to 10 per cent. on the actual cost of all the articles; this, added to the 5 per cent., makes 15 per cent. advance; that is, each article must be marked 15 per cent. higher than its present valuation in the inventory. The answer to each follows in the same order as the articles stand in the above inventory, commencing with the 3 bbls. of sugar, and finding the selling price of each per lb., &c. Note.-In marking goods, it is customary to neglect the mills, if under 5; if exactly 5, add 4 of a cent, and if over 5, add 1 cent to the cents. Calico,. .... 102 Cotton, 16 26 each 53 ..339 41 per 402 each Sugar, at.. 7 per lb. | 25 per yd. Pails, Tea,. Coffee, .575 per can. Tubs, ... Pork, 9 Knives, Beef, 8 53 Snuff, Broadcloth, 137 Ploughs, Blue do. 431 Rakes, 25 Rum, Molasses, .. 28. Brandy, 129 Brandy, ... 133 Hats,. 30 per gal. Mixed do. 126 Satin,... 101 Hymn-Books, 44 Spelling-B. 21 Geographies, 18 249 each. Geography, 138 Wine, 98 Shoes, Wine, 207 a pair. Great-Coats, 230 115 Shoes, 25... Vest, .... 574 Gin, Whips, 131 each. Hoes, Axes, 134 Hhds. 129 Axe-helves, 8 .. 52. Bought 42 gallons of rum, for $37,80; how much wates must be mixed with it, that it may be afforded for $,80 pes gallon? $,80: $37,80 :: 1 gal: 471 galls.; then, 47) = 42+ 5} galls., Ans. 53. A thief, having 30 miles the start of an officer, makes off at the rate of 8 miles an hour; the officer presses on after him at the rate of 10 miles an hour: how much does he gain on thẹ Chief in one hour? how long before he will overtake the thief! 4.2 miles; 15 hours. 54. A person, looking at his watch, was asked what o'clock It was; he replied it was between 4 and 5; but, a more particu lar answer being requested, he said the hour and minute hands were then exactly together. What was the time? See the Key L 55. At 12 o'clock the hour and minute hands of a clock are exactly together; when will they be together again? Ans. 1 h. 5 m. 27 sec. 56. If 10 men can perform a piece of work in 25 days, how many men will accomplish another piece of work, four times as large, in a fifth part of the time? A. 200. 57. A can do a piece of work in 8 days, and B in 12; in what time would both finish it by working together? Days. Day. Work. Work. *8 : 1 :: 1 : } 12 : 1 :: 1 ל1 : 58. What number is that, from which if you take, the re mainder will be ? } + 1 = 11, Ans. 59. What number is that, from which if you take, the re mainder will be ? Ans. §. 60. What number is that, from which if you take of of 2}, the remainder will be? Ans. 61. What number is that, which, being divided by, the quotient will be ? .4. 19. 62. What number is that, which, being multiplied by, the product will be 31? A. 3. 63. What number is that, from which if you take of itself, the remainder will be 12? = 1, or 4,-,, remainder. Then, the remainder 12, being 4 × 12=4 times greater than the remainder, the number itself will be 48 times greates than 1. A. 48. 64. What number is that, to which if you add of of itself, the sum will be 39 ? of, and the number itself; then, +18=18; if to the whole number of of it be added, the sum will be 18; consequently 39 is of the number. Ans. 30. 65. What number is that, to which if you add of itself, the sun will be 18? A. 12. 66. A owns of a vessel, B, C, and D the remainder; D's part is $100 can you tell me how many dollars is each man's part, and what part of the vessel D owns? Ans. A's part, $100; B's, $200; C's, $400; and D's part is 67. There is a beam, of which is in the ground, in the water, and the rest, being 2 feet, out of water; how long i the beam? A. 16 feet. 68. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled; how many were in this army? how many killed? how many taken captives? = 12 +12, of the whole army; then, as more makes 13, or the whole army, 1000; and if be 1000, how much is +, or the whole? Ans. 2400, the whole army; 800 killed, 600 cap.ives. 69. Suppose that there is a mast erected, so that of its length stands in the ground, 12 feet in the water, and of its length in the air, or above water; I demand the whole length Reducing the fractions to the least common denominator, gives 18+18=1; therefore 12 feet=18. A. 216 feet. 70. In an orchard of fruit-trees, of them bear apples, pears, plums, 40 of them peaches, and 10 cherries; how inany trees does the orchard contain? : = 50+10. Ans 600. 71. A man spent one third of his life in England, one fourth in Scotland, and the remainder, which was 20 years, in the United States; to what age did he live? A. 43 years. 72. The number of scholars in a certain school is as follows: of the pupils study geography, grammar, } arithmetic, and 10 learn to read; what number is pursuing each branch of study? A. 30 in geography, 80 in grammar, 120 in arithme tic, and 10 learn to read. 73. The double and the half of a certain number, increased by 7 inore, make 100; what is that number? A. 37. 74. A man, having purchased a drove of cattle, was driving them to market, when he was met by a gentleman, who inquired of him where he was going with his 100 head of cattle? Sir, said he, I have not near 100, but if I had as many more as I now have, as many more, and 7 cattle and, I should have a hundred. How many had he? A. 37. 75. Five eighths of a certain number exceed of the same number by 36; what is that number? -=; hence 36 is of the number sought. A. 160. 76. What number is that, which, being increased by t, §, and † of itself, the sum will be 131 ? Ans. 7349. The eleven foregoing questions are usually performed by a rule called Position, but this method of solving them by frac tions is preferable. 77. A hare starts up 12 rods before a hunter, and seuds away |