let

c = 5 years the age of Carla now

j = the age of Jim now

p = the age of Peter now

Jim is 13 yrs younger than Peter

j = p - 13

one year ago Peters age was twice the sum of Carla and Jim age

p - 1 = 2(5 - 1 + j - 1)

p - 1 = 2(3 + j)

by solving the system of equations

j = p - 13

p - 1 = 2(3 + j)

we find

j = 6 years

p = 19 years

click here to see the step by step solution of the system of equations

Carla is 5 years old now.

Jim is 6 years old now.

Peter is 19 years old now.