A Graduated Series of Exercises in Elementary Algebra: With Appendices Containing Papers of Miscellaneous Examples. Designed for the Use of Schools |
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Common terms and phrases
1st term 5abc 5th term a+b+c a²x² ab² algebraical quantity arithmetic means arithmetic series arithmetical progression bushels coefficient common difference common ratio complete square cube roots decimals denominator digits Divide equal EXERCISE Explain Find the greatest Find the least Find the number Find the sum Find the value following equations following quantities fraction gallons geometric means geometric series geometrical progression given number greatest common measure gression harmonic means harmonical progression least common multiple lowest terms meant miles Multiply PROBLEMS PRODUCING proportion Prove quotient Required the numbers result rule Show SIMPLE EQUATIONS Simplify the expression Simplify the following Solve the equations Solve the following square root Subtract third three numbers UNKNOWN QUANTITIES vulgar fractions whole number Write x²y y²)² yards
Popular passages
Page 50 - 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 95 - A ship sails with a supply of biscuit for 60 days, at a daily allowance of 1 ft. a head ; after being at sea 20 days she encounters a storm, in which 5 men are washed overboard, and damage sustained that will cause a delay of 24 days, and it is found that each man's allowance must be reduced to five-sevenths of a pound.
Page 49 - T.wo detachments of foot being ordered to a station at the distance of 39 miles from their present quarters, begin their march at the same time; but one party, by travelling...
Page 36 - A composition of copper and tin containing 100 cubic inches weighed 505 ounces. How many ounces of each metal did it contain, supposing a cubic inch of copper to weigh 5\ ounces, and a cubic inch of tin to weigh 4^ ounces? Ans. 420 of copper, and ss of tin.
Page 75 - ... 21. A cistern holding 20 barrels has two pipes, by one of which it receives 120 gallons in an hour, and by the other discharges 80 gallons in the same time ; in how many hours will it be filled ? 22.
Page 37 - ... as many men in front as there were spectators. Had the depth however been increased by 5, and the spectators drawn up in the mass with the army, the number of men in front would have been 100 fewer than before.
Page 47 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 97 - The proposition holds true of two ranks of magnitudes, whatever be their number, of which each of the first rank has to the second magnitude the same ratio that the corresponding one of the second rank has to a fourth magnitude : as is manifest.
Page 49 - A merchant bought cloth for which he paid £33 15s., which he sold again at £2 8s. per piece, and gained by the bargain as much as one piece cost him : how many pieces did he buy ? Ans.
Page 42 - ... and, if 198 be added to the number, we obtain a number with the same figures in an inverted order; what is the number? Ans. 456. 19. A farmer mixes barley at 28 cents, with rye at 36, and wheat at 48 cents per bushel, so that the whole is 100 bushels, and worth 40 cents per bushel. Had he put twice as much rye, and 10 bushels more of wheat, the whole would have been worth exactly the same per bushel ; how much of each kind was there ? Ans. Barley 28, rye 20, and wheat 52 bushels. 20. A, B, and...