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A general loses one sixth of his troops to a deadly virus. Of those that survive the virus, one fourth are killed in battle.
If there are 75 troops remaining, how many were present before the disease struck?
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x - (x/6) - (1/4)*(x - (x/6)) = 75, or
(5/6)x - (1/4)*(5/6)x = 75, or
(1 - (1/4))*(5/6)x = 75, or
(3/4)*(5/6)x = 75, or
x = 75*(6/5)*(4/3) = 120.
Answer. 120 troops.