Question

Julius has 72 cups and 64 glasses. If he will put them in a tray with the same number of cups and glasses, what is the biggest possible number of cups and glasses that the tray will contain?

Answer 1

To find the biggest possible number of cups and glasses per tray for Julius, we calculate the greatest common divisor (GCD) of 72 (cups) and 64 (glasses), which is 8. Therefore, Julius can arrange 8 trays, each with 8 items consisting of an equal number of cups and glasses.

Step-by-step explanation:

The question posed deals with finding the greatest number of cups and glasses that can be placed on a tray such that each tray contains the same number of cups and glasses. To solve this, we need to determine the greatest common divisor (GCD) of 72 (the number of cups) and 64 (the number of glasses). The GCD of 72 and 64 is 8, which means the largest number of items that each tray can hold is 8 items (a combination of both cups and glasses).

We can come to this conclusion after understanding that we can only form trays where the number of cups and glasses on each tray is equal and exact, without any cups or glasses left over. The GCD gives us the highest number of cups and glasses we can have on each tray while still maintaining the equality and ensuring no items are left over.

Using basic division, we arrive at the final arrangement: 72 cups divided by 8 equals 9 trays of cups, and 64 glasses divided by 8 equals 8 trays of glasses. Each tray would contain one cup and one glass, totaling to 8 trays containing both cups and glasses.