I did take a look at this, but I'm not making much headway.
Boyle's law applies when temperature and quantity are held
constant, but here the quantity is being changed, so it doesn't
apply. Not only that, but it relates pressure and volume, and
there are no pressure figures given.

It can be tackled by using the Universal Gas Law, PV=nRT.
If we assume constant temperature, the we can calculate the
pressure given the quantities and volumes provided, and from
there, prove Boyle's law.

The problem is that the Universal Gas was derived in part from
Boyle's law, so we would be working in some sort of backwards
circle.

The more I look at it, the more your data looks inconsistent, I'm
afraid.

First situation: 500 g of gas (which is a lot, and that makes me
suspicious) with a volume of 9.4 (what? litres?).
PV = nRT for standard units, but I'll use R' here since we don't
know the volume units and the quantity is in g, not mol, so the
constant will be different.

P1 x 9.4 = 500R'T

For the second, we have:
P2 x 8.8 = 700R'T

If the temperatures are the same then:
700/500 x P1 x 9.4 = 8.8 x P2
=> 13.16 P1 = 8.8 P2
=> P2 = 1.50 P1

Now you can do the Boyle comparison:

First situation: P1V1 = 9.4P1
Second situation: P2V2 = 1.5P1 x 8.8 = 13.2P1

Well, they are not the same at all. Let's see hat happens with
situation 3:

P3 x 8.2 = 900R'T
Compared to situation 1 at the same temperature, we have:
900/500 x P1 x 9.4 = P3 x 8.2
=> 16.92P1 = 8.2 P3
=> P3 = 2.06 P1

P3V3 = 2.06P1 x 8.2 = 16.9P1

Different again.

I see four possibilities:
I've got it totally wrong somewhere;
The temperature was not constant;
The data are flawed;
Boyle's law does not hold.

Sorry, but it looks like I can't help you on this one.