119. The area of a rectangular field is 4 acres and 35 square rods; and the sum of its length and breadth is equal to twice their difference. What are the length and breadth? 11.-15 X. = 11 120. Two travellers, A and B, set out to meet each other. They started at the same time and travelled on the direct road toward each other. On meeting it appeared that A had travelled 18 miles more than B, and that A could have travelled B's distance in 9 days, while it would have taken B 16 days to travel A's distance. How far did each travel? Ans. A, 72 miles; B, 54 miles. 121. Find three quantities such that the product of the first and second is a; of the second and third, b; and of the first and third, c. 122. A and B invest in stocks. At the end of the year A sells his stocks for $108, gaining as much per cent as B invested; B sold his for $49 more than he paid, gaining one fourth as much per cent as A. What sum did each invest? 123. Reduce 18x2 Ans. A, $45; B, $140. Ans. y2.1 ±3/1.49, or 5, org. 126. Reduce (x — x2 + 4)2 + x2= 5704+x1. 32x 844 Ans. 13, or ±2√√√2, or 13-35 +6=30 3 128. Reduce y2 - 2 √ √ y2 — 3y+5=3y-2.4 0-10: √x-2. x = 16 cul 2x2218), to find x and y. - y2 = 140 S 136. Given {5x2y—2xy2 = 875 ? 137. Given 138. Given 139. Given 140. Given { x2 y2 3xy 105 x2 y2 - 4 x y = 96}, to find x and y. (5 x2 - 3xy = 182 3y2+5xy = 132, to find x and y. = x2 + y2 + x + y = 12}, to find x and y. { x2 x +y Ans. Sx x = 2, or (−3 ±√21). 141. A drover sold a number of sheep that cost him $297 for $7 each, gaining $3 more than 36 sheep cost him. How many sheep did he sell? 66 142. A merchant sold a piece of cloth for $75, gaining as much per cent as the piece cost him. What did it cost him? 50 143. A drover bought 12 oxen and 20 cows for $920, buying one ox more for $160 than cows for $66. What did he pay a head for each? 40 cow 22 144. A started from C towards D and travelled 4 miles an hour. After A had been on the road 6 hours, B started from D towards C, and travelled every hour one fourteenth of the whole distance, and after he had been on the road as many hours as he travelled miles an hour, he met A. What was the distance from C to D? 70 145. A person bought a number of horses for $1404. If there had been 3 less, each would have cost him $39 What was the number of horses and the cost of more. each? 12 no horses· 117 cost of each 146. Find a number of four figures which increase from left to right by a common difference 2, while the product of these figures is 384. Ans. 2468. 147. A rectangular garden 24 rods in length and 16 in breadth is surrounded by a walk of uniform breadth which contains 3996 square feet. What is the breadth of the walk? Ans. 3 feet. 148. A square field containing 144 ares has just within its borders a ditch of uniform breadth running entirely round the field and covering 381.44 centares of the area. What is the breadth of the ditch? Ans. 0.8 meter. 149. A and B hired a pasture into which A put 5 horses, If B had put and B as many as cost him $5.50 a week. in 4 more horses, he ought to have paid $6 a week. What was the price of the pasture a week? Ans. $8. 150. A father dying left $3294 to be divided equally among his children. Had there been 3 children less, each would have received $183 more. How many children were there? 9 151. A merchant bought a quantity of tea for $66. If he had invested the same sum in coffee at a price $0.77 less a pound, he would have received 140 pounds more. How many pounds of tea did he buy? 60 152. Find two quantities such that their sum, product, and the sum of their squares shall be equal to one another. Ans. (33) and (3√3). 153. Find two numbers such that their product shall be 6, and the sum of their squares 13. 忆 11* 154. A and B talking of their ages find that the square of A's age plus twice the product of the ages of both is 3864; and four times this product, minus the square of B's age, is 3575. What is the age of each? Ans. A's, 42; B's, 25. 155. Find two numbers such that five times the square of the less minus the square of the greater shall be 20; and five times their product minus twice the square of the greater shall be 25. 156. A and B purchased a wood-lot containing 600 acres, each agreeing to pay $17500. Before paying for the lot, A offered to pay $20 an acre more than B, if B would consent to a division and give A his choice of situation. How many acres should each receive, and at what price an acre? Ans. A, 250 acres at $70 an acre; B, 350 at $50. 157. A merchant bought two pieces of cloth for $175. For the first piece he paid as many dollars a yard as there were yards in both pieces; for the second, as many dollars a yard as there were yards in the first more than in the second; and the first piece cost six times as much as the second. What was the number of yards in each piece? Ans. In 1st, 10 yards; in 2d, 5. 158. Two sums of money amounting to $14300 were lent at such a rate of interest that the income from each was the same. But if the first part had been at the same rate as the second, the income from it would have been $532.90; and if the second part had been at the same rate as the first, the income from it would have been $490. What was the rate of interest of each? Ans. First, 7 per cent; second, 7 per cent. 159. Divide 29 into two such parts that their product will be to the sum of their squares as 198 : 445. |