The first statement tells us the the sum of the tenths digit (t) and the hundredths digit (h) is 13. The equation for this is: t + h = 13
The second statement tells us that reversing the digits decreases the number by .45 this means that .th is .45 greater than .ht. To get .th, we need to multiply t by .1 and h by .01. From the second statement, we would get the equation: .1t + .01h = .1h + .01t + .45
To solve this, I would solve the first equation for one of the variables (I will solve for t) and substitute into the second equation.
t + h = 13
t = 13  h
.1t + .01h = .1h + .01t + .45
.1(13  h) + .01h = .1h + .01(13  h) + .45
1.3  .1h + .01h = .1h + .13  .01h + .45
1.3 .09h = .09h + .58
1.3  .58 = .09h + .09h
.72 = .18h
h = 4
Now that we have one digit, we can substitute the number into the first equation to find the other digit
t + h = 13
t + 4 = 13
t = 9
5/2/2013

John R.