$5000. They gain $840. of the gain? auction, amount to $6875; deducted for expenses, &c. the dividend? What is each man's share A.'s gain $252. Ans. B.'s gain $378. C.'s gain $210. Proof. $840. $8750, James Dole 3. A bankrupt owes Peter Parker $3610, and James Gage $7000. His effects sold at of this sum $375 are to be What will each receive of Parker $2937.75100. $1212.03. Gage $2350.2080 Ans. Dole 4. A merchant, failing in trade, owes A. $500, B. $ 386, C. $988, and D. $ 126. His effects are sold for $100. What will each man receive? Ans. A. receives $25.00, B. $ 19.30, C. $49.40, D. $6.30. Section 45. DOUBLE FELLOWSHIP. When merchants in partnership employ their stock for unequal times, it is called Double Fellowship. 1. Josiah Brown and George Dole trade in company Brown put in $600 for 8 months, and Dole put in $400 for 6 months. They gain $60. What is each man's share of the gain? Operation by analysis. We say, $600 for 8 months is the same as 8 x $600 = $4800 for 1 month; and $400 for 6 months is the same as 6 × $400 $2400 for 1 month. The question is, therefore, the same, as if Brown had put in $4800 and Dole $2400 for 1 month each. The whole stock would then be $4800 +$2400 = $7200, and Brown's share of the gain would be 4888 of $60 $ 40. Dole's share will be 100 = of $60 $20. Hence the propriety of the following = 800 7200 RULE. Multiply each man's stock by the time it continued in trade, and consider each product a numerator, to be written over their sum, as a common denominator; then multiply the whole gain or loss by each fraction, and the several products will be the gain or loss of each man. 2. A., B., and C. trade in company. A. put in $700 for 5 months; B. put in $800 for 6 months; and C put in $500 for 10 months. They gain $399. What is each man's share of the gain? Ans. A.'s gain $ 105, B.'s gain $144, C.'s gain $150. 3. Leverett Johnson, William Hyde, and William Tyler, formed a connexion in business, under the firm of Johnson, Hyde, and Co.; Johnson at first put in $ 1000, and, at the end of 6 months, he put in $500 more. Hyde at first put in $ 800, and, at the end of 4 months, he put in $400 more, but, at the end of 10 months, he withdrew $ 500 from the firm. Tyler at first put in $1200, and, at the end of 7 months, he put in $300 more, and, at the end of 10 months, he put in $ 200. At the end of the year they found their net gain to be $1000. What is each man's share? Ans. Johnson's gain $348.02338, Hyde's $273.78, Tyler's $378.19T 4. George Morse hired of William Hale, of Haverhill, his best horse and chaise for a ride to Newburyport, for $3.00, with the privilege of one person's having a seat with him. Having rode 4 miles, he took in John Jones and carried him to Newburyport, and brought him back to the place from which he took him. What share of the expense should each pay, the distance from Haverhill to Newburyport being 15 miles? Ans. Morse pays $ 1.90, Jones pays $1.10. 5. J. Jones and L. Cotton enter into partnership for one year. January 1, Jones put in $ 1000, but Cotton did not put in any until the first of April. What did he then put in to have an equal share with Jones at the end of the year ? Ans. $1333.331. Section 46. DUODECIMALS. DUODECIMALS are so called because they decrease by twelves, from the place of feet towards the right. Inches are called primes, and are marked thus '; the next division after is called seconds, marked thus " ; and so on. 1. Multiply 8 feet 6 inches by 3 feet 7 inches. OPERATION. 6 8 3 7 25 6' For As feet are the integers of units, it is evident, that feet multiplied by feet will produce feet; and, as inches are twelfths of a foot, the product of inches by feet will be twelfths of a foot. the same reason, inches multiplied by inches will produce twelfths of an inch, or one hundred and forty-fourths of a foot. Hence we deduce the following 4 11' 6" 30 5' 6" RULE. Under the multiplicand write the same names or denominations of the multiplier; that is, feet under feet, inches under inches, &c. Multiply each term in the multiplicand, beginning at the lowest, by the feet of the multiplier, and write each result under its respective term, observing to carry a unit for every 12 from each denomination to its next superior. In the same manner the multiplicand by the inches of the multiplier, and write the result of each term one place further towards the right of those in the multiplicand. Proceed in the same manner with the seconds, and all the rest of the denominations, and the sum of all the lines will be the product required. 2. Multiply 8ft. 3in. by 7ft. 9in. Ans. 63ft. 11' 3". Ans. 103ft. 4′ 5′′ 8′ 4′′. 5. Multiply 161ft. 8' 6" by 7ft. 10'. Ans. 1266ft. 8′ 7′′. 6. Multiply 87ft. 1' 11" by 5ft. 7′ 5′′. Ans. 33ft. Ans. 489ft. 8' 0" 2" 7" 7. What are the contents of a board 18ft. long and 1ft. 10in. wide? 8. What are the contents of a board 19ft. 8in. long and 2ft. 11in. wide ? Ans. 57ft. 4' 4". 9. What are the contents of a floor 18ft. 9in. long and 10ft. 6in wide? Ans. 196ft. 10' 6". 10. How many square feet of surface are there in a room 14ft. 9in. long, 12ft. 6in. wide, and 7ft. 9in. high? Ans. 791ft. 1' 6". 11. John Carpenter has agreed to make 12 shoe-boxes of boards that are one inch thick. The boxes are to be 3ft. 8in. long, 1ft. 9in. wide, and 1ft. 2in. high. How many square feet of boards will it require to make the boxes, and how many cubic feet will they contain? Ans. 280 square feet; 66 cubic feet, 864 inches. 12. My garden is 18 rods long and 10 rods wide; a ditch is dug round it two feet wide and three feet deep, but the ditch not being of a sufficient breadth and depth, I have caused it to be dug one foot deeper and 1ft. 6in. wider. How many solid feet will it require to be removed? Ans. 7540 feet. NOTE 1. A pile of wood, that is 8 feet long, 4 feet high, and 4 feet wide, contains 128 cubic feet, or a cord; and every cord contains 8 cord-feet; and, as 8 is of 128, every cord-foot contains 16 cubic feet; therefore, dividing the cubic feet in a pile of wood by 16, the quotient is the cord-feet; and, if cord-feet be divided by 8, the quotient is cords. When wood is "corded" in a pile 4 feet wide, by multiplying its length by its height, and dividing the product by 4, the quotient is the cord-feet; and, if a load of wood be 8 feet long, and its height be multiplied by its width, and the product divided by 2, the quotient is the cord-feet. NOTE 2. Small fractions are rejected in the operation. 13. How many cords of wood in a pile 56 feet long, 4 feet wide, and 5 feet 6 inches high? Ans. 9g cords. 14. How many cords of wood in a pile 23 feet 8 incheslong, 4 feet wide, and 3 feet 9 inches high? M* Ans. 2 cords 15. How much wood in a pile 97 feet long, 3 feet 8 inches wide, and 7 feet high? Ans. 19 cords 32 feet. 16. If a pile of wood be 8 feet long, 3 feet 9 inches wide, how high must it be to contain one cord ? Ans. 4 feet. 17. If a board be 1 foot 7 inches wide, how long must it be to contain 20 square feet? Ans. 12 feet 714 inches. 18. From a board 19 feet 7 inches long, I wish to slit off one square yard; how far from the edge must the line be drawn? Ans. 5 inches. 19. I have a shed 19 feet 8 inches long, 14 feet 6 inches wide, and 7 feet 6 inches high; how many cords will it contain ? Ans. 16 cords 5§ feet +. 20. I have a room 12 feet long, 11 feet wide, and 71⁄2 feet high; in it are 2 doors, 6 feet 6 inches high, and 30 inches wide, and the mop-boards are 8 inches high; there are 3 windows, 3 feet 6 inches wide, and 5 feet 6 inches high; how many square yards of paper will it require to cover the walls? Ans. 2529 square yards. Section 47. INVOLUTION. INVOLUTION is the raising of powers from any given number, as a root. A power is a quantity produced by multiplying any given number, called a root, a certain number of times continually by itself; thus, 3 3 is the first power of 3=31. = 3 x 39 is the second power of 3 = 32. 3 × 3 × 3 = 27 is the third power of 3=33. 3x3x3x3 = 81 is the fourth power of 3 = 34. |