Intellectual Algebra (Paperback)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1855 edition. Excerpt: ...equal to one third of Eliza's. How many books has each? Let x represent Eliza's number of books; then 10--x will represent Anna's number. One half of 10--x will be 5---; 2 ' but this must be equal to one third of Eliza's, or--; therefore, by the conditions of the question, X _ X 3 Y" Adding--to each member of the equation, --+-= 5. 3 ' 2 Reducing the terms of the first member to the same denomination, 6 " 6 Uniting terms in the first member, 5 x G' If one sixth of 5 z is 5, the whole of 5 x will be six times 5, which is 30. If 5 x = 30, x will be one fifth of 30, which is 6; therefore, x = 6, Eliza's books, and 10--z = 4, Anna's books. Or, bx since--= 5. b multiplying each member by 6, 5z = 30. Dividing each member of this last equation by 5, z = 6, as above. 2. The sum of two numbers is five, and one half of the less number is equal to one third of the greater What are the numbers 1 3. What is one half of the expression 10--x1 4. If the expression 10--x be divided by 2, what will represent the quotient? 5. What is one fourth of the expression 10--x1 6. If the expression 10--x be divided by 4, what will represent the quotient? 7. If 15--2x be divided by 3, what will the quotient be 1 8. John and William have seven oranges. One half of William's number is equal to two thirds of John's. How many oranges has each 1 9. The sum of two numbers is fourteen, and one half of the greater is equal to two thirds of the less number. What are the numbers? 10. A and B gained ten dollars, and one half of A's share is equal to one third of B's. How many dollars has each1 11. The sum of two numbers is eighteen, and one half of the less number is equal to one fourth of the greater. What are the numbers 1 12. The sum of the ages of Sarah and...