Opening at a different resolution to what they were scanned at

Check your scanning software settings. Scanning software usually allows you to separately set two ppi numbers.

The first is the resolution of the scan, which decides how many pixels will be used to capture each inch of the image being scanned.
The second is the ppi value assigned to the captured output image. This merely tells software such as Photoshop how big a print of the scanned image should be on paper. If viewed on screen the ppi value is ignored.

As an example a 36mm x 24mm slide scanned at 1200ppi will have 1700 x 1134 pixels.  If the output file is then assigned 300ppi it will print at 5.67 x 3.78 inches on paper.

Dave

The question is, how many pixels wide x high? A digital image file doesn't have a size - it only has pixels.

Pixels per inch (ppi) is just a way to translate pixels into a physical size or vice versa.

Once you have the pixels in the file, you can assign any ppi number you want, and this defines a physical size.

Pixels per inch.