Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. Arif has x marbles of which 20% are black and 80% are red. Babu has y marbles of which 40% are black and 60% are green. Dipu has z marbles of which 50% are black and 50% are blue. If 25% of the total marbles they have are black, what is x?
A. \(y + 3z\)
B. \(3y + 5z\)
C. \(4y + 5z\)
D. \((y+5z)/2\)
E. none of these
Explanation: (E) Total black marbles = \(0.20x + 0.40y + 0.50z\). Total marbles = \(x + y + z\). Given: Total black marbles are 25% of the total marbles: \(0.20x + 0.40y + 0.50z = 0.25(x + y + z)\). Multiply by 100 to clear decimals: \(20x + 40y + 50z = 25x + 25y + 25z\). \(40y - 25y + 50z - 25z = 25x - 20x\). \(15y + 25z = 5x\). Divide by 5: \(3y + 5z = x\). So, \(x = 3y + 5z\). Since \(3y + 5z\) is not an option, the answer is E.
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