7. Two merchants, A and B, loaded a ship with 500 hhds. of rum; A loaded 350 hhds., and B the rest; in a storm, the seamen were obliged to throw overboard 100 hhds.; how much must each sustain of the loss? Ans. A 70, and B 30 bhds. 8. A and B companied; A put in $45, and took out of the gain; how much did B put in ? Ans. $30. Note. They took out in the same proportion as they put in; if 3 fifths of the stock is $45, how much is 2 fifths of it? 9. A and B companied, and trade with a joint capital of $400; A receives, for his share of the gain, as much as B; what was the stock of each? 10. A bankrupt is indebted to A $780, to B $460, and to C $760; his estate is worth only $600; how must it be divided? Note. The question evidently involves the principles of fellowship, and may be wrought by it. Ans. A $234, B $138, and C $228. 11. A and B venture equal stocks in trade, and clear $164; by agreement, A was to have 5 per cent. of the profits, because he managed the concerns; B was to have but 2 per cent.; what was each one's gain? and how much did A receive for his trouble? Ans. A's gain was $117'142, and B's $46,8574, and A received $70'2855 for his trouble. 12. A cotton factory, valued at $12000, is divided into 100 shares; if the profits amount to 15 per cent. yearly, what will be the profit accruing to 1 share? to 2 shares ? to 5 shares? to 25 shares? Ans. to the last. $450. 13. In the above-mentioned factory, repairs are to be made which will cost $340; what will be the tax, on each share, necessary to raise the sum ? shares? on 10 shares ? on 2 shares ? on 3 Ans. to the last, $34. 14. If a town raise a tax of $1850, and the whole town be valued at $37000, what will that be on $1? What will be the tax of a man whose property is valued at $ 1780 ? Ans. $'05 on a dollar, and $89 on $1780. T 99. In assessing taxes, it is necessary to have an inventory of the property, both real and personal, of the whole town, and also of the whole number of polls; and, as the polls are rated at so much each, we must first take out from the whole tax what the polls amount to, and the remainder is to be assessed on the property. We may then find the tax upon 1 dollar, and make a table containing the taxes on 1, 2, 3, &c., to 10 dollars; then on 20, 30, &c., to 100 dollars; and then on 100, 200, &c., to 1000 dollars. Then, knowing the inventory of any individual, it is easy to find the tax upon his property. 15. A certain town, valued at $64530, raises a tax of $2259'90; there are 540 polls, which are taxed $'60 each; what is the tax on a dollar, and what will be A's tax, whose real estate is valued at $1340, his personal property at $874, and who pays for 2 polls? 540 X '60 = $324, amount of the poll taxes, and $2259'90 $324 = 1935'90, to be assessed on property. $64530: $1935'90 :: $1: '03; or, 192519003, tax on $1. Tax on 1 is '03 Tax on 10 is '30 | Tax on Now, to find A's tax, his real estate being $1340, I find, 70.. 2'10 700.. 21' 80.. 2'40 800.. 24' 90 2470 900 27 property to be 2 polls at '60 each, are In like manner I find the tax on his personal 26'22 1'20 Amount, $67'62 16. What will B's tax amount to, whose inventory is 874 dollars real, and 210 dollars personal property, and who pays for 3 polls? Ans. $34'32. 17. What will be the tax of a man, paying for 1 poll, whose property is valued at $3482? at $940? at $768? at $4657? Ans. to the last, $140'31. 18. Two men paid 10 dollars for the use of a pasture 1 month; A kept in 24 cows, and B 16 cows; how much should each pay? 19. Two men hired a pasture for $10; A put in 8 cows 3 months, and B put in 4 cows 4 months; how much should each pay? The 100. The pasturage of 8 cows for 3 months is the same as of 24 cows for 1 month, and the pasturage of 4 cows for 4 months is the same as of 16 cows for 1 month. shares of A and B, therefore, are 24 to 16, as in the former question. Hence, when time is regarded in fellowship,Multiply each one's stock by the time he continues it in trade, and use the product for his share. This is called Double Fellowship. Ans. A 6 dollars, and B 4 dollars. 20. A and B enter into partnership; A puts in $100 6 months, and then puts in $50 more; B puts in $200 4 months, and then takes out $80; at the close of the year, they find that they have gained $95; what is the profit of each? S$ 43'711, A's share. $51'288, B's share. 21. A, with a capital of $500, began trade Jan. 1, 1826, and, meeting with success, took in B as a partner, with a capital of $600, on the first of March following; four months after, they admit C as a partner, who brought $800 stock; at the close of the year, they find the gain to be $700; how must it be divided among the partners? Ans. { Ans. $250, A's share. $250, B's share. $200, C's share. QUESTIONS. 1. What is fellowship? 2. What is the rule for operating? 3. When time is regarded in fellowship, what is it called? 4. What is the method of operating in double fellowship? 5. How are taxes assessed? 6. How is followship proved? CP ¶ 101. /Alligation is the method of mixing two or more simples, of different qualities, so that the composition may be of a mean, or middle quality. (When the quantities and prices of the simples are given, to find the mean price of the mixture, compounded of them, the process is called Alligation Medial. 1. A farmer mixed together 4 bushels of wheat, worth 150 cents per bushel, 3 bushels of rye, worth 70 cents per bushel, and 2 bushels of corn, worth 50 cents per bushel; what is a bushel of the mixture worth? It is plain, that the cost of the whole, divided by the num ber of bushels, will give the price of one bushel. 4 bushels, at 150 cents, cost 600 cents. 3 at 70 .............. 210 2 at 50 9 bushels cost 100 e: 101 cts. Ans. 910 cents. 2. A grocer mixed 5 lbs. of sugar, worth 10 cents per lb., 8 lbs. worth 12 cents, 20 lbs. worth 14 cents; what is a pound of the mixture worth? Ans. 121. 3. A goldsmith melted together 3 ounces of gold 20 carats fine, and 5 ounces 22 carats fine; what is the fineness of the mixture? Ans. 21. 4. A grocer puts 6 gallons of water into a cask containing 40 gallons of rum, worth 42 cents per gallon; what is a gallon of the mixture worth? Ans. 361 cents. 5. On a certain day the mercury was observed to stand in the thermometer as follows: 5 hours of the day, it stood at 64 degrees; 4 hours, at 70 degrees; 2 hours, at 75 degrees, and 3 hours, at 73 degrees: what was the mean temperature for that day? It is plain this question does not differ, in the mode of its operation, from the former. Ans. 69 degrees. ¶ 102. When the mean price or rate, and the prices or rates of the several simples are given, to find the proportions or quantities of each simple, the process is called Alligation Alternate alligation alternate is, therefore, the reverse of alligation medial, and may be proved by it. R* 1. A man has oats worth 40 cents per bushel, which he wishes to mix with corn worth 50 cents per bushel, so that the mixture may be worth 42 cents per bushel; what proportions, or quantities of each, must he take? Had the price of the mixture required exceeded the price of the oats, by just as much as it fell short of the price of the corn, it is plain, he must have taken equal quantities of oats and corn; had the price of the mixture exceeded the price of the oats by only as much as it fell short of the price of the corn, the compound would have required 2 times as much oats as corn; and in all cases, the less the difference between the price of the mixture and that of one of the simples, the greater must be the quantity of that simple, in proportion to the other; that is, the quantities of the simples must be inversely as the differences of their prices from the price of the mixture; therefore, if these differences be mutually exchanged, they will, directly, express the relative quantities of each simple necessary to form the compound required. In the above example, the price of the mixture is 42 cents, and the price of the oats is 40 cents; consequently, the difference of their prices is 2 cents: the price of the corn is 50 cents, which differs from the price of the mixture by 8 cents. Therefore, by exchanging these differences, we have 8 bushels of oats to 2 bushels of corn, for the proportion required. Ans. 8 bushels of oats to 2 bushels of corn, or in that proportion. The correctness of this result may now be ascertained by the last rule; thus, the cost of 8 bushels of oats, at 40 cents, is 320 cents; and 2 bushels of corn, at 50 cents, is 100 cents; then, 320 +100420, and 420, divided by the number of bushels, (8+2,) = 10, gives 42 cents for the price of the mixture. 2. A merchant has several kinds of tea; some at 8 shillings, some at 9'shillings, some at 11 shillings, and some at 12 shillings per pound; what proportions of each must he mix, that he may sell the compound at 10 shillings per pound? Here we have 4 simples; but it is plain, that what has just been proved of two will apply to any number of pairs, if in each pair the price of one simple is greater, and that of the other less, than the price of the mixture required. Hence we have this |