Question

Pirate Jack has an equal number of gold and silver coins. If Pirate Jack splits all of his coins into 7 equal piles for his parrots, he has 4 coins left. Or, if he splits all of his coins into 11 equal piles for his shipmates, he has 4 coins left. Assuming every pile has at least 1 coin, what is the least possible number of coins Pirate Jack has?

Answer 1

158 coins

Explanation:

Jack's number has to be an even number, because he can split his gold and silver coins evenly.

77 is the LCM of 11 and 7 and add 4 (the remainder) to get 81.

But it has to be an even number since he can split his coins evenly.

You can then do 77 times 2, and add 4 to get 158, which is the answer.

Answer 2

The least possible number of coins that Pirate Jack has is 77.

Explanation:

i) let the number of coins in the piles for the parrots be x.

ii) therefore we can say that the total number of coins be 7x + 4

iii) let the number of coins in the piles for for the pirates be y.

iv) therefore we can say that the total number of coins be 11y + 4

v) therefore we can say that 7x + 4 = 11y + 4

vi) therefore 7x = 11y

vii) therefore the least possible number of coins that Pirate Jack has is equal to the LCM of 11 and 7 which is 77.

viii) x = 11 and y = 7