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?

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

Answer: 5, 10 and 16 y. o

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.