A Universal Key to the Science of Algebra: In which Some New Modes of Operation are Introduced Corresponding to the Cancelling System in Numbers ...

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E. Morgan & Company, 1844 - Algebra - 167 pages

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Page 73 - A gentleman bought a number of pieces of cloth for 675 dollars, which he sold again at 48 dollars by the piece, and gained by the bargain as much as one piece cost him. What was the number of pieces 1 Prob.
Page 130 - And from equation (2), 2= — 2-|-y, or #=4, and lly==44, one of the numbers, and of course 56 is the other, 8. Find a number which being divided by 6, shall leave the remainder 2, and the same number divided by 13 shall leave the remainder 3. Consider that in division, the divisor and quotient multiplied together, and the remainder added, gives the number divided. Let N represent the number divided, x and y the quotients. Then 6*+2=N, and l3y+3=N.
Page 159 - A person bought two cubical stacks of hay for 4 1 ; each of them cost as many shillings per solid yard as there were yards in a side of the other, and the greater stood on more ground than the less by 9 square yards. What was the price of each ? 69.
Page 154 - Find three numbers, such, that their product increased by unity shall be a square, also the product of any two increased by unity, shall be a square. Ans. l, 3, and 8. Assume 1 for the first number, and x and y for the other 12. Find two numbers, such that if the square of each be added to their product, the sums shall be both squares.
Page 164 - Geese, which were proceeding at the rate of 3 miles in 2 hours, he afterwards met a stage wagon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of Geese at the 45th mile stone, and met the same stage wagon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London 1 Solution.
Page 91 - What are the numbers ? Ans. 4, 12, and 36. 12. It is required to find two numbers, such, that their product shall be equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes.
Page 102 - A person travels from a certain place, goes 1 mile the first day, 2 the second, 3 the third, and so on; and in six days after, another sets out from the same place to overtake him, and travels uniformly 15 miles a day.
Page 75 - A vintner sold 7 dozen of sherry and 12 dozen of claret for 50, and finds that he has sold 3 dozen more of sherry for 10 than he has of claret for 6. Required the price of each.
Page 16 - Four places are situated in the order of the letters, A, B, C, D. The distance from A to D is 34 miles; the distance from A to B is...
Page 72 - Prob. 13. A and B distributed 1200 dollars each, among a certain number of persons. A relieved 40 persons more than B, and B gave to each individual 5 dollars more than A. How many were relieved by A and B ? Ans. 120 by A, and 80 by B.

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