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# Egg Containers

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You recently bought more than 100 eggs. The eggs are sorted in containers that can store exactly 12 eggs. However, upon inspecting the containers, you realize that two containers each hold only 11 eggs, while all the other containers hold 12 eggs. What is the smallest number of eggs you could have right now?

Nov 13, 2018

#1
+20239
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The next larger number than 100 that is divisible by 12 is 108....since you got shorted two eggs, you now have 106.

Nov 13, 2018
#2
+1

In order to have more than 100 eggs, you would have to have a minimum of:

7 cartons x 12 eggs =84 eggs

2 cartons x 11 eggs =22 eggs

84 + 22 =106 - minimum number of eggs.

Nov 13, 2018
#3
+107405
+1

We could solve this.....where N  =  the number of cartons that hold 12 eggs

2(11)  +  12N   > 100

22 + 12N >  100

subtract  22 from both sides

12N >  78      divide both sides by  12

N >  78/ 12

N  >   6.5

So.....we must have  7  cartons holding 12 eggs

So....the minimum number of eggs is

22 + 7(12)

22  + 84

106

Nov 14, 2018