Sum

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 almost 20.

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#### 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`

`47 xx <= 1161`

`x <= 24.702`

Thus the largest values of the positive interger x is 24,

Hence the required integer are 24, 25 and 26

Concept: Solving Algebraically and Writing the Solution in Set Notation Form

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