Question 843199
let your digits be a and b.


your first number is ab.
your second number is ba.


the value of your first number is 10a + b
the value of your second number is 10b + a.


assume that your second number is 75% bigger than your first number.


this means that your second number is 1.75 times as big as your first number.


since the value of your first number is 10a + b and the value of your second number is 10b + a, this means that:


10b + a is equal to 1.75 * (10a + b)


simplify this equation to get:


10b + a = 17.5 * a + 1.75 * b


subtract 1.75 * b from both sides of this equation and subtract a from both sides of this equation to get:


10b - 1.75b = 17.5a - a


simplify this to get:


8.25b = 16.5a


divide both sides of this equation by 8.5 to get:


b = 16.5a/8.25


this simplifies to b = 2a


since b has to be an integer, and b has to be 2a, then the biggest that b can be is 8.


if it were 9, than a would not be an integer.


it can't be 10 since a single digit can only go up to 9.


so the biggest that b can be is 8 and this means that the biggest that a can be is 4 which is 1/2 * b.


since your first number is ab, then that number is 48.
since your second number is ba, then that number is 84.


84 is 1.75 * 48 so the solution is good.