I am trying to figure out the cost of merchandise destroyed on Feb. 7th given the following information:

Jan 1. Merchandise inventory $144,200
Jan. 1-Feb. 7 Purchases (net) 40,000
Jan. 1-Feb. 7 Sales (net) 70,000
Estimated gross profit rate: 40%
(gross profit rate=gross profit/net sales)

I know that ending inventory is beginning+purchases-cogs, I'm not sure how to go about getting there though, and when I do, is the answer going to be 60% of what I get? I'm just not too sure the right steps to take.

You're just a couple of steps away. You have the beginning balance and the purchases, but no COGS. But you do have sales.

Keep in mind that sales and COGS is the same inventory, one at retail and one at cost. No, you can't get straight there with that, but what is sales less COGS?

Think about it.