A woman with a basket of eggs finds that if she removes the eggs from the basket 3 or 5 at a time, there is always 1 egg left. However, if she removes the eggs 7 at a time, there are no eggs left. If the basket holds up to 100 eggs, how many eggs does she have? Explain your reasoning.
Let the maximum number of eggs holds in a basket are 100
If a women removes the eggs 3 or 5 at a time the remaining egg is 1 but she removes the eggs 7 at a time there are no eggs left.
The total number of eggs she have are 91 because if the 91 eggs she removes 3 at a time she removes 30 times \(3 \times 30=90\) then 1 egg is left. If she removes 5 eggs at a time she removes
18 times \(5 \times 18=90\) then 1 egg is left. But if she removes 7 eggs at a time \(7 \times 13=91\) there are no eggs left.
Therefore, the answer is 91