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)   (Show Source): You can put this solution on YOUR website!
p, the percent carbon for the wet basis coal

Assuming start with 100 grams of the wet coal


.
.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
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  


     = 0.71.


Therefore,


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


     = 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).


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