Smart Lady Shopping

Number Theory Level pending

In the age of Renaissance, a young lady was shopping with a bag full of gold coins.

First, she visited the fish market and paid 3 gold coins for some fish. Then she started counting the remaining gold coins in her bag and realized that the number of coins was now divisible by 7.

Afterwards, she went to the nearby farm and bought some vegetables, which cost her 2 gold coins. This time, she rechecked the coins again, figuring out that the number of coins was now divisible by 6.

While walking along the street, she noticed 1 gold coin on the pavement by chance and picked up the coin with joy. The number of coins was at last divisible by 5.

On the way back home, she saw a very beautiful yet very expensive dress on display of 250 gold coins, which exceeded her budget, so she just sighed and returned home silently with her stuff.

Initially, how many gold coins did the lady have in her bag?


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