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added ADDITION ALGEBRAIC amount answered approximating arithmetical assumed balls calculated capital cards cent Class Combinations common divisor compound consequently consists contain continued fraction cost cubes denominator denote determined dice difference divided DIVISION dollars equal equation EXAMPLES exponent expressed extremes factors feet five formula fortune four fourth fraction gallons geometrical progression give given greatest half increased interest kind leave less letters logarithms means merchant miles months multiplied numbers obtain period person piece powers preceding present prime problem proportion quotient receive remainder Required to find roots shillings silver Smallest solution sought squares subtracted taken third three numbers tion twice unknown quantities values weigh whole wine wishes yearly
Page 247 - Three laborers are employed in a certain work. A and B would, together, complete this work in a days ; A and C require b days ; but B and C, only c days. What time would each require, singly, to accomplish it in, supposing, under all circumstances, that each does the same quantity of work?
Page 240 - A person had two barrels, and a certain quantity of wine in each. In order to have an equal quantity in each, he poured out as much of the first cask into the second as it already contained ; then again he poured out as much of the second into the first as it then contained ; and, lastly, he poured out again as much from the first into the second as there was still remaining in it.
Page 229 - TV, and in the fifth 450. How many had he ? Ans; 1200. 48. I once had an untold sum of money lying before me. From this, I first took away the 3d part, and put in its stead $50. A short time after, I took from the sum, thus augmented, the 4th part, and put again in its stead, $70. I then counted my money, and found $120. What was the original sum ? Ans. $25. 49. After paying away £ and ]• of my money, I had $66 left in my purse.
Page 261 - Find a number consisting of three digits, such, that the sum of the squares of the digits, without considering their position, may be 104 ; but the square of the middle Examples of 'Quadratic Equations higher than the Second Degree.
Page 212 - There is a wagon with a mechanical contrivance by which the difference of the number of revolutions of the wheels on a journey is noted. The circumference of the fore wheel is a feet, and of the hind wheel b feet.
Page 236 - A cistern containing 210 buckets, may be filled by 2 pipes. By an experiment, in which the first was open 4, and the second 5 hours, 90 buckets of water were obtained. By another experiment, when the first was open 7, and the other 3£ hours, 126 buckets were obtained. How many buckets does each pipe discharge in an hour ? Ans. The first pipe discharges 15, and the second pipe discharges 6 buckets.
Page 199 - Ans. 240 miles on horseback, 840 miles by water, and 1960 miles on foot. 15. Divide the number a into three such parts, that the second may be m times, and the third n times as great as the first.
Page 258 - A calculates that he can reach the place D in 4 days, and that B can arrive at the place C in 9 days. What is the distance between C and DI Ans.
Page 247 - C m -r— - — days. --c — be 13. A cistern may be filled by three pipes, A, B, C. By the pipes A and B, it could be filled in 70 minutes ; by the pipes A and C, in 84 minutes ; and by the pipes B and C, in 140 minutes. In what time would each pipe fill it? Ans. A in 105, B in 210, and C in 420 minutes.