I can place 8 large boxes or 10 small boxes into a carton, I sent a total of 96 boxes.
How many cartons were shipped if I sent more large boxes than small boxes?
I kind of used trial and error but my reasoning is as follows.
7 x 8 = 56 boxes. (LARGE BOXES) 7 cartons
4 x 10 = 40 boxes. (SMALL BOXES) 4 cartons
96 total boxes and 11 cartons
If anyone has a technical method they can contribute.
+129849 Let y be the number of large boxes and x be the number of small ones.
The possibilities for this problem occur in the intersection of the inrequality y > x with the equation of the line 10x + 8y = 96. as shown in this graph : https://www.desmos.com/calculator/o77ftjozeh
The only integer solutions occur at (0,12) and at (4, 7)
So.....if we require that we send at least one box of both types, the guest's answer of 4 small and 7 large cartons is correct.
However, if we don't have this requirement......it is possible that we could just ship 12 cartons filled with large boxes only.....
