49. Find the L. C. M. of 8x3 +38x2+59x+30 50. A boy spent half of his money in one shop, one-third of the remainder in a second, and one-fifth of what he had left in a third. He had 20 cents at last; how much had he at first? 51. Find the remainder when x7-10x+8x5 −7x3+3x-11 is divided by x2-5x+4. b 52. Simplify 4 (a-3(-)} {} (2a−b)+2 (b– -b)+2(b−c)} . 54. Find the L.C.M. of x2-7x+12, 3x2-6x-9, and 2x2-6x-8. 55. Find the sum of the squares of ax+by, bx− ay, ay+bx, by - ax; and express the result in factors. 2 - 4x x2 - x2 x3y—y1 ́ 60. A man agreed to work for 30 days, on condition that for every day's work he should receive $2.50, and that for every day's absence from work he should forfeit $1.50; at the end of the time he received $51: how many days did he work? 69. Find the square root of - (3b – 2c − 2a)3 {2 (a+c)−3b}. 70. The united ages of a man and his wife are six times the united ages of their children. Two years ago their united ages were ten times the united ages of their children, and six years hence their united ages will be three times the united ages of the children. How many children have they? 2 71. Find the sum of a2-3x-3y2, 2y2-y3+22, 72. From {(a+b) (a − x) − ( a − b)(b−x)} subtract (a+b)2 – 2bx. 73. If a=5, b=4, c=3, find the value of †6abc+(b+c)3+(c+a)3+(a+b)3 − (a+b+c)3. 74. Find the factors of 80. A number consists of three digits, the right-hand one being zero. If the left-hand and middle digits be interchanged the number is diminished by 180; if the left-hand digit be halved, and the middle and right-hand digit be interchanged, the number is diminished by 336: find the number. (a2b-2ab2)2, 2a2-3ab-262, and 2 (2a2+ab)2. 90. A bag contained ten dollars in dimes and quarters; after 17 dimes and 6 quarters were taken out, three times as many quarters as dimes were left: find the number of each coin. 91. Find the value of 5(a-b)-2(3a-(a+b)} +7 {(a-2b)-(5a-2b)}, 92. Divide 3xa — 5x3+7x2 – 11x – 13 by 3x – 2. - 15(p3+q3), 5(p2−P1+q2), 4(p2+pq+q2) and 6(p2 — q2). 100. The express leaves New York at 3 p.m. and reaches Albany at 6; the ordinary train leaves Albany at 1.30 p.m. and arrives at New York at 6. If both trains travel uniformly, find the time when they will meet. 101. Solve (1) 6x+·75x-·16=x— ·583x+5. a+ x 2.x3 102. Simplify (1) a2+ax+x2+ a2-ax+x2+ aa+a2x2+x4° - 20; + 1/2 − 6 (a2 + 1 ) + 15 (a2 + 1/2) also the cube root of the result. 104. Divide 1-2x by 1+3x to 4 terms. 105. I bought a horse and carriage for $450; I sold the horse at a gain of 5 per cent., and the carriage at a gain of 20 per cent., making on the whole a gain of 10 per cent. Find the original cost of the horse. 106. Find the divisor when (4a2+7ab+5b)2 is the dividend, 8 (a+26)2 the quotient, and b2 (9a+116)2 the remainder. 107. Solve (1) 5x (x-3)=2(x-7). 113. Solve 2x2+(6α-10b) x-30ab and 3x2 - (9a +15b) x + 45ab. (1) 2cx2 - abx+2abd=4cdx. |