Married filing jointly with three kids income limit to receive any earned income tax credit is $51,567. The amount of credit is based on income though. In this example filing jointly with 3 kids the credit would be higher if they earned $16,000 instead of $50,000. If they earned $5,000 instead of $16,000 it would be less too.
There is also the child tax credit is not refundable but lowers their liability. Some families may also get the additional child tax credit which is refundable.
For couples without children they may qualify for earned income credit too but the maximum credit is much less (under $500) and the income limits are lower.
I don't know how to figure federal income tax, so not sure about the specific $30,000. Their earned income credit would be over $4,000 though.
~Tiffany