Three friends Alex, Ben, and Casey presented a young mathematician with a puzzle. They told him that the sum of

Question

their ages add up to 98 years. Double Alex’s age and add to Ben’s gives 84 years. The sum of three times Alex’s age
and twice Casey’s age is 163. Find the ages of Alex, Ben and Casey

Answer 1

The sum of their ages add up to 98 years --> a+b+c=98

Double Alex’s age and add to Ben’s gives 84 years
2a + b = 84

The sum of three times Alex’s age and twice Casey’s age is 163
---> 3a + 2c = 163

form 2a+b = 84 ---> b = 84-2a

I would now plug that into the first equation, to have only a and c
the third equation has only a and c
solve those, then back-substitute