Math problem - Algebra

Question

It is known that each of the seven players in a handball team are of a different age. The captain is the oldest. It is also known that the total sum of all their ages is 150.

What is the minimum possible age of the captain?

Answer 1

7 players, total age = 150

captain is the oldest, what is his minimum possible age?

if the Captain is 18, then the average age of the other 6 is (150-18)/6 = 132/6 = 21, then he's not the oldest

150/7 = 21 3/7 is their age if all are the same. The captain's youngest possible age is slightly over 21 3/7 with everyone else slightly less than 21 3/7 years old.

If you restrict the ages to integer values, then 6 are 21 years old and the captain is 150-6(21) = 150-126 = 24

Then the captain's youngest age seems to 24 years old

or if one is 22, five 21, then C = 150-5(21)-22 = 150-127 = 23

Captain's youngest age is 23