SOLUTION: A coal contains 2.4% of water. After drying, the moisture-free residue contains 71.0% carbon. Determine the percentage of carbon on "wet basis". All percentage are by weight.

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Question 1121497: A coal contains 2.4% of water. After drying, the moisture-free residue contains 71.0% carbon. Determine the percentage of carbon on "wet basis". All percentage are by weight.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
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p, the percent carbon for the wet basis coal

Assuming start with 100 grams of the wet coal

%28100%2A%280.01%29p%29%2F%28100-2.4%29=0.71
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Answer by ikleyn(52786) About Me  (Show Source):
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Let M be the mass of the coal before drying.


Since it contains 2.4% of water, after drying the mass will be  M - 0.024*M.


Let C be the mass of carbon in this coal.


Then the condition says  


    C%2F%28M+-+0.024%2AM%29 = 0.71.


Therefore,


    C = 0.71*(M-0.024*M) = 0.71*M*(1-0.024),   or


    C%2FM = 0.71*(1-0.024) = 0.693 (approximately),   or  69.3%.


Answer.  Before drying, the percentage of carbon in the coal is  69.3%, approximately (rounded to one decimal place).