Here's how I'm assigning a different variable to the value of each digit:
10x + y, where x is the first digit, and y is the second digit (you can test if this equation works)
The sum of the digits is 1/5 the value of the number. Using the information, we can form the equation:
x + y = (1/5)(10x + y)
Simplify
x + y = 2x + (1/5)y
The tens digit is one less than the ones digit. Using this information, we can form the equation:
x = y - 1
Adding both sides by 1 gives
x + 1 = y
Substituting this into the y's the first equation gives:
x + x + 1 = 2x + (1/5)(x + 1)
Distribute and simplify
2x + 1 = 2x + (1/5)x + 1/5
Subtract both sides by 2x
1 = (1/5)x + 1/5
Subtract 1/5 from both sides
4/5 = (1/5)x
Multiply both sides by 5
4 = x
x = 4
Use this to solve for y
x + 1 = y
4 + 1 = y
y = 5
Thus, x = 4 and y = 5. The 2 digit number is XY, which is 45.
Let me know if you need any clarifications; this was a very interesting math problem to solve!
