Algebra Puzzle – Challenge 49

Challenge:

John wants to clean his house during this week. He cleaned (frac{1}{5}) of his house on Sunday and (frac{1}{4}) of the remaining on Monday. On Tuesday, John cleaned ( frac{1}{3}) of what still remained and (frac{1}{2}) of what left on Wednesday. What fraction of the house needs to be cleaned?

A- (frac{1}{5})

B- (frac{1}{6})

C- (frac{1}{12})

D- (frac{1}{16})

E- (frac{1}{24})

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John cleaned (frac{1}{5}) of his house on Sunday and (frac{1}{4}) of the remaining on Monday.
The remaining on Monday was (frac{4}{5}). Therefore, (frac{1}{4}) of (frac{4}{5}) equals:
(frac{1}{4} × frac{4}{5} = frac{4}{20} = frac{1}{5}). So, he cleaned (frac{1}{5}) of his house on Sunday and another (frac{1}{5}) of his house on Monday. The remaining for the next day is (frac{3}{5}) of the house.
On Tuesday, John cleaned (frac{1}{3}) of what still remained. (frac{1}{3}) of (frac{3}{5}) of the house equals:
(frac{1}{3} × frac{3}{5} = frac{3}{15} = frac{1}{5}). So far, he has cleaned (frac{3}{5}) of the house and (frac{2}{5}) of the house is left.
He cleaned (frac{1}{2}) of what left ((frac{2}{5}) of the house) on Wednesday. (frac{1}{2}) of (frac{2}{5}) of the house equals:
(frac{1}{2} × frac{2}{5} =frac{2}{10} = frac{1}{5}).
Therefore, (frac{1}{2}) of the house needs to be cleaned.

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