Question

The present ages of Andy and Mike are in the ratio 5 : 3. If Andy had been 7 years older and Mike 7 years younger, the age of Andy would have been 3 times the age of Mike. Find their present ages.

Answer 1

Let Andy be $5x$ years old and let Mike be $3x$ years old.

If Andy had been 7 years older, the age of Andy would have been $5x+7$.

If Mike had been 7 years younger, the age of Andy would have been $3x-7$. 

Also we know that age of Andy would have been 3 times the age of Mike:

$5x+7=3(3x-7)$

$5x+7=9x-21$

$28=4x$

$x=7$

$5x=5\cdot7=35$ and $3x=3\cdot7=21$

Answer: Andy is 35 years old and Mike is 21 years old.