Question

Jim is half his mother's age. His mother is 5 years younger than his father, in total their ages are 100 years. What is Jim's age?

Answer 1

Jim is 19

let fathers age be x then mothers age = x - 5 and Jim's age is $\frac{1}{2}$(x - 5)

Total their ages and equate to 100

x + x - 5 + $\frac{1}{2}$(x - 5 ) = 100

multiply through by 2 to eliminate the fraction

2x + 2x - 10 + x - 5 = 200

5x - 15 = 200 ( add 15 to both sides )

5x = 215 ( divide both sides by 5 )

x = 43

father is 43 years, mother is 38 and Jim is 19