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