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<<<What's the best way
to invest the proceeds from the sale of her house to attempt to cover the remaining $800 each month without
exhausting the entire $60,000?>>>

Much depends on your mother's age/life expectancy, but in just about any instance, it's not going to be easy.

You need $9600 per year. Being conservative and laddering 5 years worth into CDs, or $48000, that would leave $12000 to invest elsewhere. This amount isn't large enough to throw off money to replace your yearly costs, unless of corse you're able to double your money every year. Therefore, I'd probably keep it all in CDs.

Another option, invest the 60k in stocks and with a 5% drawdown would generate around 3k/yr or $250/month and you come up with the extra $550/month. In about 5-7 years, the investments might be throwing off $500/month and you'd half to come up with $300 and maybe by 10-12 years it'd be able to generate it all.
This later approach is obviously more risky. But if your mother in younger, 65-70? and in relative good health, she could live 15-20 years and you'd have to take a little more risk so as to not outlive the money, or outlive as quickly. If she's older and in poor health and not expected to live more than 5 years, be conservative.

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