Whole Number P5 A001

The Lim family are great mathematicians. When asked how old everyone is, the family replies:

"Our family of 2 adults and 3 children are 100 years old together. The sum of the father's age and the son's age is 51. The father is 3 years older than the mother while the twin daughters are each 5 years younger than the brother."

What are their ages?

Firstly list out all the information (relationships) given.

Our family of 2 adults and 3 children are 100 years old together

(F + M) + (S + D1 + D2) --> 100

The sum of the father's age and the son's age is 51.

F + S --> 51

The father is 3 years older than the mother

F --> M + 3

the twin daughters are each 5 years younger than the brother

D1 = D2 --> S – 5

Then, replace D and F with S and M respectively.

(M + 3) + M + S + (S – 5) + (S – 5) --> 100

2 M + 3 S --> 100 – 3 + 5 + 5 = 107

M + S --> 51 – 3 = 48

M + 2 S --> 107 – 48 = 59

Next, solve for M or S, then follow by the other unknowns.

S --> 59 - 48 = 11

D --> 11 – 5 = 6

M --> 48 – 11 = 37

F --> 37 + 3 = 40

The father, mother, son and twin daughters are 40, 37, 11 and 6 years old respectively.