# Tom And The Cartons - Math Riddle

In the world of shipping logistics, Tom faces a unique challenge involving the arrangement of small and large boxes into cartons for an important shipment. With specific box capacities per carton and a total count of boxes dispatched, a fascinating mathematical puzzle arises, prompting us to explore the solution behind determining the number of cartons shipped.

Tom is in charge of shipping and he can place 10 small boxes or 8 large boxes into a carton. A total of 96 boxes were sent in one shipment. The number of small boxes was less than large boxes. What is the total number of cartons he shipped?

Explanation :

If we take into account that Tom shipped both large as well as small boxes in the cartons.

If a total of 96 boxes are shipped then the large boxes in the cartons must be a multiple of 8 which means either 16 or 56 large boxes are there.

But according to the question that there are more large boxes in the cartons then the small ones, so the number of large boxes must be 56.

And therefore the number of small boxes are reduced to 96 - 56 = 40

So the total number of cartons shipped are:

56/8 + 40/10 = 7 + 4 = 11

Through mathematical analysis and considerations of box ratios and constraints, Tom determined that he shipped a total of 96 boxes in 9 cartons to efficiently pack both small and large boxes. This problem-solving exercise highlights the importance of efficient packaging and logical reasoning in the realm of logistics.