Question
A bag contains ‘x + 2’ red, ‘x + 4’ blue and
‘2x – 2’ green Gloss papers. Two papers are randomly drawn from the bag, so the probability that a blue paper and a green paper are drawn is 4/15. Determine the total number of papers in the bag.Solution
According to question: x+4C1 × 2x-2C1/ 4x+4C2 = 4/15 2(x + 4) × (2x – 2)/{(4x + 4) × (4x + 3)} = 4/15 (x + 4)(x – 1)/{(x + 1)(4x + 3) = 4/15 15x2 + 45x – 60 = 16x2 + 28x + 12 x2 – 17x + 72 = 0 x2 – 9x – 8x + 72 = 0 x(x – 9) – 8(x – 9) = 0 (x – 9)(x – 8) = 0 x = 8, 9 So the total number of papers in the bag = either 4 × 8 + 4 = 36 or 4 × 9 + 4 = 40
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