Ruby is 6 times older than Sam. In 9 years, Ruby will be 3 times as old as Sam. How old is Sam now?
How old is Ruby now? ** Let x be Sam's age and Y be Ruby's age. Ruby's age is currently 6 times Sam's age, so 6 * x = Y years.
How old will Ruby be in 9 years? ** In 9 years Ruby's age will be 3 times Sam's age, so, 3 * (x + 9) = (Y + 9) years.
How old will Ruby be in 9 years? ** To find out Sam's age, we substituted the first step in the second to get 3 * (x + 9) = (6 * x) + 9.
How old will Ruby be in 9 years? ** We distribute on one side of the equation to get (3 * x) + 27 = (6 * x) + 9.
How old will Ruby be in 9 years? ** We isolate Sam's age on one side of the equation to get 27 - 9 = (6 * x) - (3 * x).
How old will Ruby be in 9 years? ** We simplify the equation to get 18 = 3 * x.
How old is Sam now? ** Now we know that Sam's age is 18 / 3 = <<18/3=6>>6 years.
#### 6