How many crates will there be?

Question

I’m working on the following riddle:

UPS can fit 8 large packages or 10 small packages in a crate for shipping. In one shipment, they can send a total of 96 packages. If there are more large packages than small packages in a shipment, how many crates can they ship?

Here’s what I have so far. I’m not so sure it’s correct, though:

L + S = 96

L > S

L/8 + S/10 = C (# of crates)

When you plug this into WolframAlpha, you get:

L > 48

S = 96 - L

C = (L + 384)/40, therefore they can send a maximum of (49+384)/40 crates (>=10.825 crates).

Answer 1

The answer is

12

The reason for this is as follows:
You want to minimize the crates of small packages. This is because you can fit more crates with large packages. The most minimal it could be is 0... this would result in 96 large packages and 0 small. 96>0 so all constraits are filled. 96 large packages takes up 12 crates.