You are transporting a large number of eggs to the White Hou

You are transporting a large number of eggs to the White House for their annual Easter Egg Roll, but you forgot how many eggs you have. You know you have fewer than 1000. You try placing them in cartons of 12, but there are 8 left over. You then try placing them in buckets that hold 7 eggs each, but there are 5 left over. Finally, you place them in baskets that hold 11 eggs each, and they fit perfectly, filling every basket. How many eggs do you have?

Solution

X<1000

X = 12k1+8

X=7k2+5

So, 60k1 = 56k2

or 15k1 = 14k2

k1 and k2 are multiple of 14 and 15 respectvely.

X=11k3

Since from eqn 1 we know the numbers going to be a mutiple of 4 and according to 3rd eqn its a mutiple of 11, then the number of total eggs must be mutiple of 44k.

So, we start with 44. and try mutiples of 44 and so on...

we get 572 as the number.

So, we had 572 eggs in the basket.