follows: his services for the two last years, at $3 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 e Y can make o 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, commenc ing with the first on the inventory, so as to clear the 5 cent. per The pupil will find, by calculation, that the expenses amount to 10 per cont. 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 solling price of each per lb. &c. Note. In marking goods, it is customary to neglect the mills, if under 5, if exactly 5, add of a cent, and if over 5, add 1 cent to the conts. Sugar, at (7) per 15. Ares, at (134) each. Hhis.. at Tea, Coffee, (575) can. Calico, Silk, (129) each. (26) ...: Pork, (9) Cotton, Beef, (8) Hams, (15) Tallow, (114) (16)... Cotton Plaid, (22) Linen, (53) .. Kettles, (339) Rum, (30) gal. Blue do. (431) Knives, (194) Ploughs, (404) each. (41) per 15. Molasses, (28) Mixed do. (126) Rakes, (25) Brandy, (129) (101) Hymn-Books,44) Brandy, Vestings, (92) patt. Wine, . (98) Hats, (2491) each. Wine, (115) Shoes, (207) a pair. Gin, (63) Shoes, (25) Vinegar, (29) Whips, (131) cach. (95) Barrels,. (86) each. Hoes, 52. Bought 42 gallons of rum for $37,80; how much water must be mixed with it, that it gallon? may be afforded for $,80 por $,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. 4t the rate of 10 miles an hour: how much does he gain on the chief in one hour? how long before he will overtake the thiefi 1.2 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? In 1 hour the minute hand passes over 12 spaces, while the hour hand passes over only 1 space at is, the minute hand gains upon the hour hand 11 spaces in 1 hour; comse quently, i must gain 12 spaces before both will be together. 60 m 11 = 51⁄2-m., gain in 1 hour; then, 55m. × 4 hours=219m, past 4 o'clock, Ans Or, the ratio being of an hour, hence, 4 hours = 21 minutes past 1, Ans., as before. 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. 27131 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? 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 3, the re mainder will be ? Ans. . 60. What number is that, from which, if you take § of 1 of 2), the remainder will be ? Ans. = 61. What number is that, which, being divided by, the quotient will be ? A. 19. 62. What number is that, which, being multiplied by , the product will be 31? A. 32. 63. What number is that, from which, if you take of itself, the remainder will be 12? 1, or,-1,-1, remainder. Then, the remainder 12, being 4X 12=48 times greater than the remainder, the number itself will be 48 times greater than 1. A. 48. 64. What number is that, to which, if you add off of itself, the sum will be 39? of, and the number itself 18; then, +18=18; & Lo the whole number of of it be added, the sum will be ; consequently 39 is of the number. Ans. 30. 65. What number is that, to which if you add of itself, the sum 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 is 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? }+&=√2, of the whole army; then, as more makes, or the whole army, 11⁄2=1000; and if be 1000, how much 15 13, or the whole? Ans. 2400, the whole army; 800 killed, 600 captives. 69. Suppose that there is a mast erected, so that of its length stands in the ground, 12 fect 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 s +18 =1; therefore 12 feet 1. A. 216 feet. 70. In an orchard of fruit trees, of them bear apples, pears, plums, 40 of them peaches, and 10 cherries; how many 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. 48 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 more, 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 af 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 number by 36; what is that number? -; hence 36 is = of the saynı of the number sought. A. 160. 76. What number is that, which, being increased by,, and of itself, the sun will be 131? Ans. 73-197. The eleven foregoing questions are usually performed by a rule called Position, but this method of proving them by fractions is preferable. 77. A hare starts up 12 rods before a hunter, and scuds away at the rate of 10 miles an hour; now, if the hunter does not change his place, how far will the hare get from the hunter in 45 seconds? A. 52 rods. 78. If a dog, by running 16 miles in one hour, gain on a hare 6 miles every hour, how long will it take him to overtake her, provided she has 52 rods the start? A. 97 seconds. 79. A hare starts 12 rods before a greyhound, but is not perceived by him till she has been up 45 seconds; she scuds away at the rate of 10 miles an hour, and the dog after her at the rate of 16 miles an hour; what space will the dog run before he overtakes the hare? A. 138 rods, 3 yards, 2 feet. 80. A gentleman has an annuity of $2000 per annum; I wish to know how much he may spend daily, that, at the year's end, he may lay up 90 guineas, and give 20 cents per day to the poor of his own neighbourhood? A. $4,128. 81. What is the interest of $600 for 120 days? (12) For 2 days? (20) For 10 years, 10 mo. and 10 days? (391) For 5 years, 5 mo. and 5 days? (19550) For 6 years, 6 mo., days? (23460) For 4 years, 4 mo. and 4 days? (15640) and 6 A. Total, $989,70. 82. What is the present worth of $3000, due 22 years hence, discounting at 6 per cent. per annum? A. $2608,695+. 83. Suppose A owes B $1000, payable as follows; $200 in 4 mo., $400 in 8 mo., and the rest in 12 mo.; what is the equated time for paying the whole? A. 8 months. 84. How many bricks, 8 inches long, 4 inches wide, and 2 inches thick, will it take to build a house 84 feet long, 40 feet wide, 20 feet high, and the walls to be 1 foot thick? The pupil will perceive that he must deduct the width of the wall, that is, 1 foot, from the length of each side, because the inner sides are 1 foot less in length than the outer sides. A. 105408 bricks. APPENDIX. ALLIGATION. * LXXXII. Alligation is the method of mixing several simples of Ferent qualities, so that the compound, or composition, may be of a mean of Vile quality. When the quantities and prices of the several things or simples are given, to the mean price or mixture compounded of them, the process is called ALLIGATION MEDIAL. A farmer mixed together 2 bushels of rye, worth 50 cents a bushel, 4 shels of corn, worth 60 cents a bushel, and 4 bushels of oats, worth 30 eo's bushel: what is a bushel of this mixture worth? ia this example, it is plain, that, if the cost of the whole be divided by ewhole number of busheis, the quotient will be the price of one bushel of the nixture. $4,60 RULE. Divide the whole cost by the whole number of bushels &-c., the quotient will be the mean price or cost of the mixture. 2. A grocer mixed 10 cwt, of sugar at $10 per cwt, 4 cwt. at $4 per cwt., and 8 cwt. at $7 per cwt.: what is 1 cwt. of this mixture worth? and what is 3 cwt. worth? A. 1 cwt. is worth $8, and 5 cwt. is worth $40. 3. A composition was made of 5 los. of tea, at $1 per lb., 9 lbs. at $1,80 per lb., and 17 lbs. at $14 per lb.: what is a pound of it worth? A. $1,546,7+. 4. If 20 bushels of wheat, at $1,35 per bushel, be mixed with 15 bushels of rye, at 85 cents per bushel, what will a bushel of this mixture be worth? A. $1,135,+. 5. If 4 lbs. of gold of 23 carats fine be melted with 2 lbs. 17 carats fine, bat will be the fineness of this mixture? A. 21 carats. ALLIGATION ALTERNATE. ↑ LXXXIII. The process of finding the proportional quantity of each simple from having the mean price or rate, and the mean prices or rates of the several simples given, is called Alligation Alternate, consequently, it is the reverse of Alligation Medial, and may be proved by it. 1. A farmer has oats, worth £5 cents a bushel, which he wishes to mix with corn, worth 50 cents per bushel, so that the mixture may be worth 30 cents per bushel; what proportions or quantities of each must he take? In this example, it is plain, that, if the price of the corn had been 35 cents that is, had it exceeded the price of the mixture, (30 cents,) just as much as it |