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annum arithmetic mean arithmetic series arithmetical progression Binomial Theorem brandy bushels cask cent cistern coefficients common difference compound interest Continued fractions cost cube digits distance equal filled Find a number Find the number Find the square Find the sum Find the value Find three following equations four numbers gallons geometric series geometrical progression guineas half harmonic harmonic means harmonic series horse least number less miles an hour miles per hour minutes multiplied number of combinations number of permutations number of terms number of variations numbers in arithmetic odd number oxen proportion prove quantity quotient ratio remainder Required the number scale sheep shew shillings Show Solve the following square number square root th term third three numbers travelled weights wheat whole number yards
Page 72 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.
Page 70 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...
Page 78 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards ; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space. Required the circumference of each.
Page 76 - There was a cask containing 20 gallons of brandy ; a certain quantity of this was drawn off into another cask of equal size, and this last filled with water, and afterwards the first cask was filled with the mixture. It now appears that if 6§ gallons of the mixture be drawn off from the first into the second cask, there will be equal quantities of brandy in each.
Page 69 - There is a field in the form of a rectangular parallelogram, whose length exceeds the breadth by 16 yards; and it contains 960 square yards. Required the length and breadth. Ans. 40, and 24 yards. 4. A person being asked his age, answered, If you add the .square root of it to half of it, and subtract 12, there will remain nothing.
Page 86 - Find two numbers such that their sum shall be equal to the sum of their squares.
Page 75 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Page 75 - A traveller set out from a certain place, and went 1 mile the first day, 3 the second, 5 the next, and so on, going every day 2 miles more than he had gone the preceding day. After he had been gone three days, a second sets out, and travels 12 miles the first day, 13 the second, and so on. In how many days will the second overtake the first ? Ans. In 2, and 9 days.