how much would they spend if their number were doubled, in 8 months ? Ans. $320. 27. If 12 men build a wall 100 ft. long, 4 ft. high, and 3 ft. thick, in 40 days; in what time will 6 men build one, 20 ft. long, 6 ft. high, and 4 ft. thick? FELLOWSHIP. The Rule of Fellowship, is a method of ascertaining the respective gains or losses of individuals engaged in joint trade. Let the pupils perform the following sums as a mental exercise. 1. Two men own a ticket; the first owns 4, and the second owns of it; the ticket draws a prize of 40 dol. lars; what is each man's share of the money? 2. Two men purchase a ticket for 4 dollars, of which one man pays 1 dollar, and the other 3 dollars; the ticket draws 40 dollars; what is each man's share of the money ? 3. A and B bought a quantity of cotton; A paid $100, and B $200 ; they sold it so as to gain $30; what were their respective shares of the gain ? The value of what is employed in trade is called the Capital, or Stock. The gain or loss to be shared is called the Dividend Each man's gain or loss is always in proportion to his share of the stock, and on this principle the rule is made. RULE. As the whole stock is to each man's share of the stock, so is the whole gain or loss, to his share of the gain or loss. 4. Two persons have a joint stock in trade ; A put in $250, and B $350 ; they gain $400 ; what is each man's share of the profit? What is fellowship? What is stock? Dividend? What is the rule? $ 50., OPERATION. 600: 250 :: 400: $166.6663 A's gain. Whole stock $600 ) 600: 350 :: 400: $233.333} B's gain. The pupil will perceive that the process may be contracted by cutting off an equal number of ciphers from the first and second, or first and third terms; thus, 6 : 250 : : 4 : 166.666}, &c. It is obvious the correctness of the work may be ascer. tained by finding whether the sums of the shares of the gains are equal to the whole gain; thus, $166.6661+ $233.333}=$400, whole gain. 5. A, B, and C, trade in company: A's capital was $175, B's 200, and C's $500; by misfortune they lose $250; what loss must each sustain ? A's loss. Ans.$ 57.1424, B's loss. $142.8571, C's loss. 6. Divide 600 among 3 persons, so that their shares may be to each other as 1, 2, 3, respectively. Ans. $100, $200, and $300. In assessing taxes, it is customary to obtain an inven. tory of every man's property, in the whole town, and also a list of the number of polls. Each poll is rated at a tax of a certain value. From the whole tax to be raised, is taken out what the tax on polis amounts to, and the re. mainder of the tax is to be assessed on the property in the town. 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 lax upon his property. 1. 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 pro. perty 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, 31=,03, tax on $1. 66 ,12 TABLE. dolls. dolls. Tax on 1 is ,03 | Tax on 10 is ,30 | Tax on 100 is 3, 2“ ,06 20 “ ,60 200 " 6, 3",09 30 “ ,90 300 “ 9, 4.6 40 5 1,20 400 - 12, 56,15 50 ~ 1,50 500 6 15, 6 ",18 60 - 1,80 600 “ 18, 76,21 70 - 2,10 700 6 21, 8“,24 80 - 2,40 800 • 24, 9“,27 90 6 2,70 900 - 27, 1000 - 30, Now, to find A's tax, his real estate being $1340, I find by the table, that The tax on $1000 is 30, 9, 1,20 $40,20 In' like manner I find the tax on his personal? 26,22 property to be 2 polls, at ,60 each, are 1,20 Amount, $67,62 2. 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 3. What will be the tax of a man paying for 1 poll, whose property is valued at $3482 ? -at $768? Ans. to the last, $140.31 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? 4. 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 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. The shares of A and B, therefore, are 24 to 16, as in the former ques. tion. Hence, when time is regarded in fellowship,Multiply each one's stock by the time he continues in the trade, and use the product for his share. This is called Double Fellowship Ans. A 6 dollars, and B 4 dollars. 5. 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 ? $51,288 6. 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 ? $250, A's share. Ans. {$250, B's share. $200, C's share. ALLIGATION. The rule of Alligation teaches how to gain the mean value of a mixture that is made by uniting several articles of different values. Alligation Medial, teaches how to obtain the value, (or mean price,) of a mixture, when the quantities and prices of the several articles are given. RULE. As the whole mixture is to the whole value, so is any part of the composition, to its mean price. EXAMPLES. 1. A farmer mixed 15 bushels of rye, at 64 cents a bushel, 18 bushels of Indian corn, at 55 cts. a bushel, and What is the rule when time is regarded in Fellowship? What is Alli. gation? What is Alligation medial? What is the rule ? 21 bushels of oats, at 28 cts. a bushel ; I demand what a bushel of this mixture is worth ? bu. cls. $ cts. bu. $ cts. bu. 15 at 6459,60 As 54 : 25,38 : :1 18 5559,90 1 21 28=5,88 -cts. 54)25,386.47 Ans. 54 25,38 2. If 20 bushels of wheat at 1 dol. 35 cts. per bushel, be mixed with 10 bushels of rye at 90 cents per bushel, what will a bushel of this mixture be worth ? Ans. $1,20 cts. 3. A tobacconist mixed 36 lbs. of tobacco, at 1s. 6d. per lb., 12 lbs. at 2s. a pound, with 12 lbs. at ls. 10d. per ib. ; what is the price of a pound of this mixture ? Ans. ls. 8d. 4. A grocer mixed 2 C. of sugar at 56s. per C. and 1 C. at 43s. per C. and 2 C. at 50s. per C. together; I de. mand the price of 3 cwt. of this mixture ? Ans. £7. 138. 5. A wine merchant mixes 15 gallons of wine at 4s. 2d. per gallon, with 24 gallons at 6s. 8d. and 20 gallons at 6s. 3d. ; what is a gallon of this composition worth? Ans. 58. 10d. 244 qrs. Alligation Alternate, teaches how to find the quantity of each article, when the mean price of the whole mixture, and also the prices of each separate article are known. RULE. Reduce the mean price and the prices of each separate article to the same order. Connect with a line each price that is less than the mean price, with one or more that is greater ; and each price greater than the mean price, with one or more that is less. Write the difference between the mean price, and the price of each separate article, opposite the price with which it is connected, then the sum of the differences, standing against any price, will express the relative quantity to be taken of that price. What is Alligation alternate ? What is the rule ? |