The University Algebra

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Sheldon & Company, 1866 - Algebra - 528 pages


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Page 390 - Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third.
Page 354 - 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 240 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 309 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately ? Ans.
Page 237 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes ; but the denominator being doubled, and the numerator increased by 2, the value becomes f?
Page 309 - If the square of a certain number be taken from 40, and the square root of this difference be increased by 10, and the sum be multiplied by 2, and the product divided by the number itself, the quotient will be 4.
Page 203 - A farmer has a stack of hay, from which he sells a quantity, which is to the quantity remaining in the proportion of 4 to 5. He then uses 15 loads, and finds that he has a quantity left, which is to the quantity sold as 1 to 2. How many loads did the stack at first contain ? 10. There are 3 pieces of cloth, whose lengths are in the proportion of 3, 5, and 7 ; and 8 yards being cut off" from each, the whole quantity is diminished in the proportion of 15 to 11.
Page 311 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.
Page 204 - 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 to the distance from C io D as 2 to 3.
Page 371 - A travels 1 mile the first day, 2 the second, 3 the third, and so on; B travels 20 miles the first day, 18 the second, 16 the third, and so on.

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