Struggling to calculate profit from a sales figure

Hello sir,

I have a question regarding calculating profit from sales of inventory. The question is about finding the value of costs of goods destroyed but to correctly solve it you need to find a figure for the costs of goods sold by deducting profit from the sales figure. Here is the full question below.

Orlean Flames is a shop which sells clothes. on 1st January 20X5 it had trade inventory which cost $7345. During the 9 months to 30 September 20X5 the business purchased goods from suppliers costing $106420. Sales during the same period were $154000. The shop makes gross profit of 40% on cost of everything it sells. On 30 September 20X5 there was a fire which destroyed most of the inventory in it. Only $350 of inventory was undamaged and fit for sale. How much inventory was lost in the fire?

As the question states gross profit of 40%, I proceeded to take 40% of the sales figure of $154000 which gave me a profit of $61600 and therefore a cost of goods sold value of $92400.

However the answer provided to me is this:

sales (140%) 154000
gross profit (40%) 44000
cost of goods sold (100%)110000

I am confused because I thought the method of working provided by the answer is the way you calculate profit using the mark-up method. Have I read the question wrong or is the working incorrect?

Many thanks