Richard is 6 years older than Lisa and in 5 years the sum of their ages will be twice as much as the sum of their ages 4 years ago. Find their present ages.?

Let Lisa's current age be ( x ). Then Richard's age is ( x + 6 ). In 5 years, their ages will be ( x + 5 ) and ( x + 11 ), respectively. The equation for their ages in 5 years is ( (x + 5) + (x + 11) = 2[(x - 4) + (x + 2)] ). Simplifying this gives ( 2x + 16 = 2(2x - 2) ), leading to ( 2x + 16 = 4x - 4 ). Solving for ( x ), we find ( x = 10 ) (Lisa's age) and ( x + 6 = 16 ) (Richard's age). Thus, Lisa is 10 years old and Richard is 16 years old.