Question

A woman with a basket of eggs finds that if she removes the eggs from the basket at 5 or 11 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

Answer 1

Answer:

56

Step-by-step explanation:

I knew that the answer would a multiple of 7, and be one more than a multiple of 5 and 1 more than a multiple of 11. I looked at the multiples of 7 to find one that was true for all of that.

Proof that 56 is correct:

First we will take 11 away until we have a remainder.

56-11=45

45-11=34

34-11=23

23-11=12

12-11=1

When we take a way 11 at a time there is always 1 egg left.

Now check for the remainder when taking away 5.

56-5=51

51-5=46

46-5=41

41-5=36

36-5=31

......

6-5=1

When we take a way 5 at a time there is always 1 egg left.

56 is divisible by 7 so there will be no eggs left when removing 7 eggs at a time.