SOLUTION: Find a 2 digit Number such that 4 times the unit digit is 5 greater than thrice the ten digit,when the digits are reversed,the number is increased by 9...find the original number?
Question 992372: Find a 2 digit Number such that 4 times the unit digit is 5 greater than thrice the ten digit,when the digits are reversed,the number is increased by 9...find the original number? Answer by solver91311(24713) (Show Source):
If the digits of a two digit number are reversed and the result is a larger number (..., the number is increased...), then the tens digit of the original number must be smaller than the ones digit. Furthermore, if the difference between the original number and the reversed digits number is 9, then the difference between the two digits is 1. (The difference between the original number and the reversed digits number is always a multiple of 9, and the multiplier is the difference between the digits. E.g. 47 reversed is 74 and these two numbers differ by 27 which is 3 times 9, whereas 4 and 7 differ by 3).
Hence we begin with, assuming represents the ones digit and represents the tens digit:
Which is to say:
And then we are given that:
Solve the 2X2 system by substitution.
John
My calculator said it, I believe it, that settles it
