John R. answered • 05/02/13

John R: Math, Science, and History Teacher

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