A department store paid $$48\mathrm{.}43$ for a salad bowl. Overhead expense is $13\%$ of the regular selling price and profit is $25\%$ of the regular selling price. During a clearance sale, the set was sold at a markdown of $18\%.$ What was the operating profit or loss on the sale?

If total costs are greater than the clearance price, then there is an operating loss by that amount. If the clearance price is greater than total costs, then there is an operating profit by that amount.

Begin by determining the selling price. The selling price must cover the cost of buying the goods, the overhead expenses of the business, and any profits required by the business.

Selling price $=$ Cost $of$ Buying $+$ Expenses $+$ Profit

Selling price $=48\mathrm{.}43+13\%$ Selling price $+25\%$ Selling price

Selling price $=48\mathrm{.}43+0\mathrm{.}13$ Selling price $+0\mathrm{.}25$ Selling price

Isolate the selling price on the left side of the equation.

Selling price $-0\mathrm{.}13$ Selling price $-0\mathrm{.}25$ Selling price $=$$$48\mathrm{.}43$

$(1-0\mathrm{.}13-0\mathrm{.}25)$ Selling price $=$$$48\mathrm{.}43$

Selling price $=$$

$($Round to six decimal places as needed.$)$