A store in Vancouver has operating expenses of 30% of the selling price and the operating profit is 50%

Question

A store in Vancouver has operating expenses of 30% of the selling price and the operating profit is 50% of the selling price. During a sale, their watches were marked down by 40%. What is the profit or loss at the sale price if they purchased the watches at $774 each?

Express the answer as a positive number for profit and negative number for loss, rounded to the nearest cent

Answer 1

Here's my try at it.

I'm assuming that operating expenses (rent, salaries, etc) do not include cost of sales.

Then Profit = Revenue - Operating Expenses - COS

Using the percentages given: 0.50SP = SP - 0.30SP - COS

COS = SP - 0.80SP = 0.20SP

SP = COS/0.20

If that's true, then the watches purchased at $774 would sell for 774/0.20 = $3,870 before the mark-down.

$3,870 - 40% is a sale price of $2,322.

Operating expenses based on regular price are 0.30(3870) = $1,161 (I decided not to base it on the reduced price).

So profit at the $2,322 sale price would be $2,322 - $774 - $1,161 = $387

I'm interested to see other people's take on this question!