Question
A container holds a mixture of two liquids, A and B, in
the ratio 2:3. If the total volume of the mixture is 70 liters, how many liters of liquid A must be added to make the ratio of A to B equal to 3:2?Solution
Current volumes: A = (2/5) * 70 = 28 liters; B = (3/5) * 70 = 42 liters. Let x be the amount of A to be added. (28 + x) / 42 = 3/2 Cross-multiplying: 2(28 + x) = 3 * 42 56 + 2x = 126 2x = 70 → x = 35 liters
I. 6y2 – 23y + 20 = 0
II. 4x2 – 24 x + 35 = 0
I. 117x² + 250x + 117 = 0
II. 54y² -123y + 65 = 0
The equation x2 – px – 60 = 0, has two roots ‘a’ and ‘b’ such that (a – b) = 17 and p > 0. If a series starts with ‘p’ such...
I. 3p² + 13p + 14 = 0
II. 8q² + 26q + 21 = 0
I. 6 y² + 11 y – 7= 0
II. 21 x² + 5 x – 6 = 0
I. x2 – 18x + 81 = 0
II. y2 – 3y - 28 = 0
I.8(x+3) +Â 8(-x) =72Â
II. 5(y + 5) + 5(-y) = 150Â
I. 22x² - 97x + 105 = 0
II. 35y² - 61y + 24 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 2x² - 8x + 6 = 0
Equation 2: y² - 7y + 10 = 0
I. 10x2 + 33x + 9 = 0
II. 2y2 + 13y + 21 = 0
