Question

find three consecutive largest positive integers such that the sum of one third of first ,one fourth of 2nd and one fifth of third is at most 20

Answer 1

Consecutive numbers are numbers which follow each other with a difference of 1 between them.

Let the first number be x

The second number = x + 1

The third number = x + 2

A third of the first = 1/3x

One fourth of the second = 1/4x + 1/4

One fifth of the third = 1/5x + 2/5

The sum of these should be at most 20.

This means it should not be more than 20:

1/3x + 1/4x + 1/5x + 1/4 + 2/5 = 47/60x + 13/20

47/60x + 13/20 ≤ 20

Lets now solve for x :

20 × (40x) + 13 × 60 ≤ 20 × 20 × 60

80x + 780 ≤ 24000

80x ≤ 24000 - 780

80x ≤ 23220

x ≤ 290.25

290.25, 291.25, 292.25