Five years ago, Tim’s mom was three times Tim’s age today. Now their combined ages are 45. How old is Tim’s mom today?

x = mom age now    t = Tims age now

(x-5) = 3(t)

and

x + t =45

   t = 45-x     sub this in to the first equation

(x-5) = 3(45-x)

x-5 = 135 - 3x

4x = 140

x = 35= Mom's age now

Let Tim's age today  = x

Five years ago his mom's age was 3x

So....her age now is  3x+ 5

So

3x+ 5 + x  = 45

4x + 5 = 45

4x = 40

x = 10

And her age now is   3(10)+ 5  =  35