If 100 soldiers had 3 injuries, and 10 soldiers had 4 injuries, wouldn't that make

3*100 + 4*10 = 340 injuries?

This does not seem right.

Steve

There are 100 soldiers total, meaning that 90 have 3 injuries and 10 have 4 injuries.

You are double counting. Your math suggests that you have 100 soldiers with 3 injuries (and, yes, a soldier with 4 injuries does have 3), BUT then you say that there are an additional 10 soldiers, who each have 4 injuries.

You can either say there are 90 soldiers with exactly 10 injuries, and 10 with exactly 4, or say there are 100 soldiers with at least 1, 2, and 3 injuries, and an additional 10 soldiers with an least 4 injuries. Thus:

3*90 + 4*10 = 310 injuries

100 + 100 + 100 + 10 = 310 injuries