Currently, Sam's coach is three times older than Sam. When Sam started soccer 15 years ago, his coach was six times his age. How old is Sam now?

Question

anonymous · Answer

Can set this up with variables x and y. X = Sam's Age, Y = Coach's Age. 
Our first equation: 3X = Y
 second equation: 6(X-15) = Y - 15, Let us expand this equation: 6X - 90 = Y - 15, or 6X - 75 = Y.
 
Now let us set these equations equal to each other: 6X - 75 = Y and 3X = Y, 
so 6X - 75 = 3X
 3X = 75, X = 25 - so at current age Sam is 25 years old and his Coach is 75 years old.

anonymous · Answer

thanks

anonymous · Answer

You can double check by subtracting 15 from both ages and seeing if Sam's age (10) multiplied by 6 is equal to the Coachs age (minus 15) - which it is: 60.
 
Sam is 25 currently not 30. People seem to forget that 15 years ago Sam's coach was also 15 years younger.