Intellectual Algebra, Or, Oral Exercises in Algebra: For Common Schools in which All the Operations are Limited to Such Small Numbers as Not to Embarrass the Reasoning Powers, But, on the Inductive Plan to Lead the Pupil Understandingly Step by Step to Higher Mental Efforts ...

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Paine & Burgess, 1845 - Algebra - 212 pages
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Page 186 - The sum of two numbers is 6, and the sum of their 5th powers is 1056. What are the numbers?
Page 139 - There are two numbers, sucti that three times the greater and twice the less, when added, are twentytwo, and twice the greater is six more than three times the less. What are the numbers ? Let x = the greater number, and y = the less number. (1.) By one condition of the question, 3 x -)- 2 y = 22.
Page 115 - The sum of two numbers is a, and their difference is b; what are the numbers? Let x — the greater number, and
Page 187 - The sum of two numbers is 32, and if the greater be divided by the less, the quotient will be less than 5 but greater than 2.
Page 187 - What are the numbers 1 9. The greater of two numbers divided by the less, is equal to the less, and the difference of their squares is 72. What are the numbers ? 10. A travelled 5 miles less than B, and the product of the distances both travelled is 84 miles. How many miles did each travel ? 11. What is that fraction which will be equal to...
Page 35 - Therefore, by the conditions of the question, 6z = 24; and, dividing each member by 6, x =^ ; that is, x is ^ of 24, which is 4. Then he bought 4 apples, 4 lemons, and 4 oranges. 15. The sum of three numbers is sixty-three. The first is twice the second, and the second is twice the third. What are the numbers ? 16. A horse, saddle, and bridle, together, cost one hundred and forty-four dollars. The saddle cost twice as much as the bridle, and the horse three times as much as the saddle and bridle...
Page 162 - RESIDUAL quantity, -is equal to the square of the first term, — twice the product of the two terms, -|- the square of the last term.
Page 99 - What are the parts ? 20. A man and boy received thirteen dollars for a week's labor. If two thirds of what the man received be taken from twice the sum that both had, the difference will be five times the money which the boy received. How many dollars had each ? SECTION XXI.
Page 170 - If 1 be added to the square of a number, the sum will be 50. What is the number ? 2. If 5 be subtracted from a number, and 1 be added to the square of the remainder, the sum will be 10. What is the number ? 3. One of two numbers exceeds 50 by as much as the other is less than 50, and their product is 2400. What are the numbers ? 4. The product of two consecutive...
Page 62 - How many sheep does each own ? 13. The sum of three numbers is seventy. The first is eleven more than the third, and the second is as much as the first and third together, lacking twelve What are the numbers ? 14. Three men together have eighty-two dollars. A has fifteen more than B, and C has as many as A and B both. How many dollars has each ? 15. Henry, William, and Robert, together, have forty-two cents. Henry has eight more than William, and Robert has only six less than both. How many cents...

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