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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?

Guest Nov 13, 2018
 #1
avatar+14543 
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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.

ElectricPavlov  Nov 13, 2018
 #2
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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.

Guest Nov 13, 2018
 #3
avatar+92608 
+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

 

 

cool cool cool

CPhill  Nov 14, 2018

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