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Question
Find three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of third is at most 20.
Solution
Let the required integers be x, x + 1 and x + 2.
According to the given statement,
`1/3 x + 1/4 (x + 1) + 1/5 (x + 2) <= 20`
`(20x + 15x + 15 + 12x + 24)/60 <= 20`
`47x + 39 <= 1200`
`47x <= 1161`
`x <= 24.702`
Thus, the largest values of the positive interger x is 24.
Hence, the required integer are 24, 25 and 26.
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