How much does it typically cost to have a dog put to sleep?

I have to decide whether to put my 16-year-old dog to sleep. She has cancer, and we’ve been helping her feel better for a while, but lately, she’s been having more bad days than good.

The vet said it would cost $624 to put her to sleep and have her cremated privately. Is this normal? I’m not sure how to ask other places about the price without feeling strange. Any suggestions would help.