I love doing recreational math! I'm not trying to "debunk" the comic or anything, I just think this is fun
Assuming this is fifth edition D&D, there are a variety of ways you could derive an exchange rate between gold pieces and USD. My favorite is the cost of living, since that accounts for any discrepancies between availability/supply/demand of particular goods, and cuts right down to how much it costs to live a given lifestyle.
I make roughly $20,000 a year, which places me squarely in the "modest" section. I don't go hungry or thirsty, my living conditions are clean and simple, and I'm able to maintain my equipment. In 5e, this costs me 1 gp per day. I can't put much into savings, so I earn 365 gp/year.
$20,000/365 ≈ 54 USD per gold piece. I'm rounding it down to $50 because it's easier. That $150 might buy them a couple days off work which is.. more of a vacation than I've had in years



