70. From a certain sum of money one-third part was taken and $50 put in its stead. From the sum thus increased one-fourth part was taken and $70 put in its stead. If the amount was now $120, find the original sum. 71. Find the lowest common multiple of (a* - a2c2)2, 4a6 - Sa1c2+4a2c4, a++3a3c+3a2c2 + ac3. 74. What must be the value of x in order that (a + 2x)2 a2+70ax +3x2 may be equal to 13 when a is equal to 67 ? 75. Find the highest common factor of 16x4+36x2+81 and 8x+27; and find the lowest common multiple of 8x3+27, 16x+36x2+81, and 6x2-5x-6. 76. Solve the equations: (1) a(x− a)-b(x − b) = (a + b)(x − a − b). (2) (a+b)x -- ay = a2, (a2 + b2)x - aby = a3. 77. A farmer bought a certain number of sheep for $30. He sold all but five of them for $27, and made a profit of 20 per cent. on those he sold: find how many he bought. 79. Find the H.C. F. of 21x3 - 26x2+8x and 6a2x3 - a2x2 - 2a2x. Also the L.C. M. of x3-x, ax2+2ax-3a, x3-7x2+6x. 80. Simplify the expression (a+b+c)(a−b+c) - {(a + c)2 − b2 − (a2 + b2 +c2)}. 84. A bag contains 180 gold and silver coins of the value altogether of $144. Each gold coin is worth as many cents as there are silver coins, and each silver coin as many cents as there are gold coins. How many coins are there of each kind? 86. Find the factors of (1) 20a2+21ab - 27b2; (2) x3-3x2-- 9x+27. 87. If the length of a field were diminished and its breadth increased by 12 yards, it would be square. If its length were increased and its breadth diminished by 12 yards, its area would be 15049 square yards. Find the area of the field. 95. A person being asked his age replied, "Ten years ago I was five times as old as my son, but twenty years hence he will be half my age." What is his age? 97. When a = 4, b = −2, c = d=-1, find the value of 3 2' 101. What value of x will make the sum of equal to 2? x+5b and 2(a - b) 3(a+b) 102. A man drives to a certain place at the rate of 8 miles an hour; returning by a road 3 miles longer at the rate of 9 miles an hour he takes 7 minutes longer than in going: how long is each road? 103. Find the product of (1) 3x2-4xy + 7y2, 3x2+4xy+7y2; (2) x2 - 2y2, x2 - 2xy + 2y2, x2+2y2, x2+2xy+2y2. 104. Extract the square root of 105. Find the highest factor common to 106. x(6x2 – 8y2) − y(3x2 - 4y2) and 2xy(2y − x)+4x3 − 2y3. The sum of the digits of a number is 9, and if five times the digit in the tens' place be added to twice the digit in the units' place, the number will be inverted. What is the number? 108. Solve the equations: (1) (x+7)(y-3) + 2 − (y+3) (x − 1) = 5x − 1ly + 35 = 0 ; 109. If x=b+c, y = c−a, z = a − b, find the value of x2 + y2+z2 - 2xy - 2xz+2yz. 110. Express in the simplest form 1 + 1 + 1 + |