Question 856453: A person removing 2 eggs at a time from an Easter basket has 1 egg left, the person removing them 3 at a time has 2 left, the person removing them 5 at a time has left. What is the fewest number of eggs possible in the basket?
I began by writing trying to compare equations, let x be the eggs in the basket before removal"
x-2=1
x-3=2
x-5=3
Combining the equations gives you 3x-10=5 -> 3x=15 -> x=5?
Is this correct, or am I doing it wrong?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! there are three different numbers not just one x
Assuming 3 left for the person 5 eggs at a time
2x+1=a,
3y+2=a,
5z+3=a
5's 8,13, 18,23
We see that it must end in 3 or 8
2's can't end in 8
must end in 3
3's 5, 8, 11 ,14, 17, 20,23
2's 3, 5, 7, 9, 11,13, 15, 17, 19, 21, 23
2
23 is 2*11+1
23 is 3*7+2
23 is 4*5+3
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