a number consists of two digits. one of the digits is greater than the other by 5 when the digits are reversed the number becomes 3 divided by 8 of the original number. find the number

The number is 72.

Step-by-step explanation:

Let the digits be x and x - 5 where x  is the first digit.

(As the number reversed = 3/8 of the original number the first digit must be the largest),

Consider the reverse digit number:

The original number = 10x + (x - 5) so the reverse number is 10(x - 5) + x and

10(x - 5) + x  = 3/8(10x + (x - 5))

11x - 50 = 3/8(11x - 5)      

11x - 50 = 33/8 x - 15/8              Multiply through by 8:

88x - 400 = 33x - 15

55x = 385

x = 7

and x-5 = 2.

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