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A $229,000 mortgage on a $277,000 property is an 82% loan-to-value (LTV) ratio. So, you have some wiggle room in obtaining a second (these usually max out at 90% LTV).
My first question would be where is the other $48,000 coming from for the purchase? If it’s cash, then you will have no problem getting a home equity loan for about $20,000 with your remaining equity (up to the 90% LTV). If you came up with the $48,000 with a second mortgage, you’re already at 100% LTV and, particularly with blemished credit, I doubt you’ll be able to get the additional funds.
The fact that you were approved for $40K over the purchase price means nothing. A bank is only going to lend up to the value of the house and, in today’s mortgage industry situation, I would be surprised if anyone were willing to go over 90% LTV.