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?

Sam is 25 years old and his Coach is 75 years old.

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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.

You can double check by subtracting 15 from both ages and seeing if Sam's age (25-15=10) multiplied by 6 is equal to the Coach's age (75-15) - which it is: 60.

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Another pair of equations in the present:

C = 3S

C-15 = 6(S-15) and substitute 3S for C

3S - 15 = 6S - 90

3S = 6S - 75

3S = 75

S = 25, C = 75