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:
The least possible number of coins pirate Jack has is 77.
Explanation:
Let the number of coins in the piles for the parrots be x.
So, the total number of coins be 7x + 4-----------(1)
Let the number of coins in the piles for for the pirates be y.
Their total number of coins will be 11y + 4-----------(2)
Both the number of coins are equal. So equating the equation (1) and (2)
7x + 4 = 11y + 4
7x = 11 y
Thus the least possible number of coins that Pirate Jack has is equal to the LCM of 11 and 7.
LCM of 11 = 11
LCM of 7 = 7
LCM of 11 and 7 = 77