increased by 10, and the sum be multiplied by 2, and the product divided by the number itself, the quotient will be 4. Required the number. Let the number. If we take the square of x from 40, we shall have This square root, increased by 10, becomes 40 240x2+20= 4 x, by multiplying by x, and 40-x2 + 10 = 2 x, by dividing by 2. 40x22x-10, by transposition. 40 To free this equation from the radical quantity, 40 x2, we must raise both members to the second power. The second power of a quantity affected with the radical sign, is evidently that quantity without the sign; fora, being the square root of a, the product of a multiplied by a must be a. Therefore, the second power of the whole equation, when raised to the second power, becomes 40 x2 is 40 40 x24x2 40 x + 100. x2; and 30. What number exceeds its square root by 42? 31. A school-boy, being asked the ages of himself and sister, replied, that he was 6 years older than his sister; and that twice the square of her age was 47 less than the square of his own. What were their ages? 32. A gentleman has two square flower-plots in his grounds, which together contain 2120 yards; and the diameter of the larger plot exceeds that of the smaller by 12 yards. What are the sides of each? 33. A laborer, having built 105 rods of fence, found that, had he built 2 rods less a day, he would have been 6 days longer in completing the job. How many rods did he build per day? 34. A farmer sold 7 calves and 12 sheep for 50 dollars; and the price received for each was such, that 3 more calves were sold for $10 than sheep for $6. What was the price of each? 1 35. A young lady, being asked her age, answered, "If you add the square root of my age to half of my age, the sum will be 12." What was her age? 36. A trader bought some barrels of flour for $60. Had he bought 3 more barrels for the saine sum, each barrel would have cost him one dollar less. How many barrels did he buy? 37. A man had a field whose length exceeded its breadth by 5 rods. He gave 3 dollars a rod to have it fenced; and the whole number of dollars was equal to the number of square rods in the field. Required the length and breadth of the field. 38. Says A to B, "I have 9 dollars more than you; and if the number of dollars we both have, be multi plied by the number that I have, the product will be 266." How many dollars has each? 39. A man has three children, A, B and C; A being the oldest, and C the youngest. Now, the difference of A and B's ages exceeds the difference of B and C's by 6 years. The sum of all their ages 33 years, and the sum of their squares 467. Required their ages. Let x B's age, is y = C's age, and x + y +6 = A's age. x + x − y + x + y + 6 = 33, by the question, or 3 x 33-6, or 27, and x 9. Again, according to the question, the sum of the squares of all their ages is 467; that is, x2 + (x − y)2 + (x + y + 6)2 = 467, or, by involution and addition, 3x2 + 2 y2 + 12 x + 12 y +36=467; 243 +2 y2 + 108 + 12 y + 36 = 467, 40. A farmer soldo 80 bushels of wheat and 100 bushels of rye for £65; and each at such a rate, that he sold 60 bushels more of rye for £20 than of wheat for £10. What was the price of each? CHAPTER XII. MISCELLANEOUS QUESTIONS. 1. A GENTLEMAN bought three kinds of wine, of each an equal quantity. For the sherry he gave $8 a dozen; for the port, $9; and for the madeira, $11. The whole came to $168. How many dozen of each kind did he buy? 2. A steam-boat has 81 passengers; there being twice as many women as children, and three times as many men as women. What is the number of men, women and children? 3. Divide $9289 between A and B in such a manner, that A's share shall be to B's as 2 to 5. 4. A man, dying, left an estate valued at $14832. In his will he gave of his property to his wife; and directed the remainder to be so divided between his son and daughter, that the daughter's portion might be to the son's as 3 to 5. What was the share of each? 5. What is that number, to which if you add of itself, and from the sum subtract of itself, of the remainder is 3? 6. A farmer bought 12 sheep, 5 cows, 2 yoke of oxen and 3 horses, for 795 dollars. A cow cost as much as 6 sheep, a yoke of oxen as much as 3 cows, and a horse as much as 3 oxen. What did he give for each? 7. A man divided a certain sum of money equally between his son and daughter; but had he given his son 33 dollars more, and his daughter 47 dollars less, her share would have been but of his. What was 言 the sum divided? 8. Divide 46 dollars into two such parts, that of one and of the other may be 10 dollars. 9. A man divided 198 acres of land between his three children in such a manner, that A's part was to B's in the ratio of 3 to 8; and C had as many acres as both his brothers. What was the share of each? 10. A man bought a certain quantity of wine for 94 dollars; and after 7 gallons had leaked out, he sold of the remainder, at cost, for $20. How many gallons did he buy? 11. If a certain number be divided by the sum of its digits, the quotient will be 8; but if the digits be inverted, and that number divided by 2 less than their difference, the quotient will be 9. What is the number? 12. Two friends bought a horse together; and when one had paid and the other of the price agreed upon, they still owed 21 dollars. What was the price of the horse? 13. In a certain university there are 384 students, of whom belong to the academical department; and in the departments of law, divinity and medi |