Answer:
Debt to income ratio is all your debt payments divided by all the money you earn during a month. Generally you are considered to be in good financial shape when your debt to income ratio is less than 20%, if it's less than 10% it is even better.
Kim's gross income = $1,230 - $165 (taxes) = $1,065
Kim's total debt payments without new debt = $134 (credit card payments)
Kim's total debt payments including new debt = $134 + $172 (new debt) = $306
Kim's debt to income ration without new debt = $134 / $1,065 = 12.58%
Kim's debt to income ration with new debt = $306 / $1,065 = 28.73%
Currently Kim's debt to income ratio is only 12.58% which is very good, but if she takes the new loan then her ratio will increase to 28.73% which is extremely high and not prudent.