14. Required the value of x in the following equation; 3 23 x 216. Multiply by 4 times the coefficient of x2, that is, by 4 × 3 = 12. 36 x2 + 36 x = 2592. Add the square of 3, the coefficient of x. No 36 x2 + 36 x + 9 = 2601, or 6x+3= 51. 15. What is the value of x in the following equa tion; 3 x2 19x=- 6? 36 x2 - 228 x 36 x2 = 72, by multiplying by 12. 228 x + 361 = 289, by adding 192. 4 x2 3 3 4 x233x, by removing the denominators. 4 x2 64 x2 16 x x 33, by transposition. 64 x2 16x + 1 = 17. There are two 528, by multiplying by 16. numbers whose difference is 9, and their product is 10 more than the square of the smaller number. What are the numbers? 18. The length of a room exceeds its width by 9 feet; and its area is 400 feet. What are the dimensions of the room? SECTION III Questions producing Affected Equations. 1. The ages of a man and his wife amount to 42 years, and the product of their ages is 432. What is the age of each? 2. A gentleman, being asked the ages of his son and daughter, replied, that his son was 5 years older than his daughter, and that the product of their ages was 266. What were their ages? 3. The length of a room exceeds its width by 8 feet, and its area is 768 feet. What are its length and width? 4. The difference of two numbers is 6; and the square of the greater exceeds twice the square of the less by 47. Required the numbers. 5. A gentleman divided 28 dollars between his two sons in such a manner, that the product of their shares was 192. What was the share of each? 6. The wall which encloses a rectangular garden, is 128 yards long, and the area of the garden is 1008 yards. What are its length and breadth? 7. A man bought a certain number of sheep for 80 dollars. If he had bought 4 more for the same money, they would have come to him a dollar apiece cheaper. How many did he buy? 8. It is required to find two numbers, whose sum shall be 14; and such, that 18 times the greater shall be equal to 4 times the square of the less. 9. A man paid 120 dollars more for his watch than for a chain; and the price of the watch was to that of the chain as the price of the chain was to 10. Requined the price of each. 10. In a parcel containing 24 coins of silver and copper, each silver coin is worth as many pence as there are copper coins; and each copper coin is worth as many pence as there are silver coins; and the whole is worth 18s. How many coins are there of each sort? 11. A drover bought a number of oxen for 675 dollars; which he sold again for 48 dollars a head; and he gained, by the bargain, as much as he gave for How many oxen did he buy? one ox. 12. Two travellers, A and B, set off at the same time to a place distant 150 miles. A travels 3 miles an hour faster than B, and arrives at his journey's end 8 hours and 20 minutes before him. How many miles did each travel per hour? 13. What two numbers are there, whose sum is 25 and product 144? 14. The age of A is 12 years more than that of B; and the product of their ages is 640. What is the age of each? 15. The sum of two numbers is 30; and if 18 be added to of their product, the sum will be equal to the square of the smaller number. What are the numbers? 16. Says A to B, "The product of our ages is 120; and if I were 3 years younger, and you were 2 years older, the product of our ages would still be 120." What are their ages? 17. A farmer sold a certain number of sheep for £120. If he had sold 8 more for the same money, he would have received 10 shillings less for each sheep. How many did he sell? 18. Two benevolent gentlemen, A and B, distributed each 1200 dollars among a certain number of poor persons. A relieved 40 persons more than B; but B gave 5 dollars more to each person than A. How many persons did each relieve? 19. A person bought two pieces of cloth; the finer of which, at 4 shillings a yard more than the other, cost £18. But the coarser piece, which was 2 yards longer than the finer, cost only £16. How many yards were there in each piece? and what was the price of a yard of each? 20. An officer would arrange 1200 men in a solid body, so that each rank may exceed each file by 59 How many must be placed in rank and file? men. 21. In an orchard containing 900 trees, the trees are so planted that there are 11 more rows than there are trees in a row. Required the number of rows; also the number of trees in a row. 22. The perimeter of a room is 48 feet; and the area of the floor is equal to 35 times the difference of its length and breadth. What are the dimensions of the room? 23.. A drover bought a number of sheep for 190 dollars. Having lost 8 of them, he must sell the remainder at a profit of 8 shillings apiece, not to lose money by the bargain. How many sheep did he buy? and at what price? 24. A merchant sold a quantity of sugar for £56, by which he gained as much per cent. as the whole cost him. How much did it cost? 25. A trader sold a quantity of flour for 39 dollars, and gained as much per cent. as the flour cost him. What did he give for the flour? 26. A butcher bought a certain number of calves for 200 dollars; and, reserving 15, he sold the rest for 180 dollars, by which he gained 2 shillings a head. How many calves did he buy? and at what price? 27. A grass-plot, 18 yards long and 12 wide, is surrounded by a border. of flowers of a uniform width. The areas of the grass-plot and border are equal. What is the width of the border? 28. A square court-yard has a gravel walk round it. The side of the court wants 2 yards of being 6 times the breadth of the walk; and the number of square yards in the walk, exceeds the number of yards in the periphery of the court by 164. What is the area of the court? 29. If the square of a certain number be taken from 40, and the square root of their difference be |