There are 15 plates in the kitchen cabinet. The diameter of each plate is either 9 inches or 12 inches. The diameter of all 15 plates combined is 150 inches. Which system of equations can be used to find the number of 9-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?

Step-by-step explanation:

The important thing to remember here is that the number of plates is a different equation from the one that uses the diameter of the plates. The number of plates will make up one equation; the diameter of the plates will make up the other equation. As far as the number of plates go, we have 15 total. Let's call the 9" plates x and the 12" plates y according to the instruction given. If we have a mixture of 9 and 12 inch plates and we have a total of 15 plates, the first equation regarding the number of plates is

x + y = 15

Now on to the diameters. The 9" plates are x's and the 12" plates are y's and the inches refer to the diameter, of which the total is 150". Therefore, the second equation regarding the diameter of the plates is

9x + 12y = 150

Those 2 equations make up the system. It doesn't say you have to solve it, but if you did, you would find that there are 10 9" plates and 5 12" plates in the cabinet.