My water pressure gauge usually read 40 psi when the water was off. Now it reads 10 psi with the water faucets off. However, the flow of the water when the water is turned on seems the same as it always was in the past. It comes out of each faucet in a strong stream. This makes me think the gauge is broken but the pump and the rest of the system is OK. Does this seem correct?

Sure sounds right. I would start by replacing the gauge and see what happens. If the pressure was actually down to 10psi, you would notice it right away at the fixtures. Please let us know how things go.

Probably your pressure tank has a little air valve at the top, like on a car tire. Use a tire pressure gauge to check pressure there. It should agree with the system gauge.

Sure sounds like a faulty gage. Their inexpensive so simply replace the gage. Good luck, Tom