Jim, carla and tommy are members of the same family. carla is 5 years older than jim. tommy is 6 years older than carla. the sum of their three ages is 31 years. how old is each one them?

So,

We'll solve it with only one placeholder, since that's simpler.

Jim's age = J
Carla's age = C
Tommy's age = T

J = base
Carla's age = J + 5
Tommy's age = Carla's age + 6 or J + 5 + 6 or J + 11

Sum of ages = 31
(J) + (J + 5) + (J + 11) = 31

3J + 16 = 31

Subtract 16 from both sides
3J = 15

Divide both sides by 3
J = 5

Carla's age = J + 5
Carla's age = 10

Tommy's age = Carla's age + 6
Tommy's age = 10 + 6 or 16

5 + 10 + 16 = 31
15 + 16 = 31
31 = 31 This checks.

Jim is 5.
Carla is 10.
Tommy is 16.

Lets
Jim  x years old
Carla (x+5) years old
Tommy (x+5)+6 years old
sum is x+(x+5)+(x+5)+6=31 years old
3x+16=31
3x=15
x=5 - age of Jim
x+5=5+5=10 - age of Carla
x+5+6=16  - age of Tommy
5, 10 and 16 y.o