Hi everyone.
Today we're going to look at an example to show application for markup and markdown.
Let's look at an example.
A retailer purchased a bike for $120.
If the expenses were set as 40% of the regular selling price, and the profit was 30% of the
regular selling price.
A- What was the regular selling price for the bike?
B- During a promotion, the bike was marked down 25%.
what was the sale price?
Also, what was the operating profit or loss during the promotion?
Let's look at the question A first.
The regular bike selling price covers the cost, expenses, and the profit.
So in this formula, S stands for regular selling price, C is for cost, E is for expenses, P
is for profit.
Regular selling price is unknown.
That's what we're looking for.
But we do know cost.
Cost is $120.
Expenses, we don't know, but we know expenses were set as 40% of the regular selling price.
Forty percent is 0.4, so 40% of regular selling price.
And the profit, again unknown, but we know it's 30% of the regular selling price.
Thirty percent, you can write as 0.3,, 30% of selling price.
Now this is an equation with one variable, S, so S is unknown.
We need to solve it.
Let's move S, all the terms with S, to the left hand side.
So S plus 0.4S, you need to change it to minus and the plus 0.3S, move it over, change to
minus.
And then we leave the number 120 to the right.
Now S, you can consider that as a 1 S.
So on the left hand side I have 1 minus 0.4 minus 0.3, times S. To the right, is 120.
I do the calculation here as 0.3 S is 120.
On both sides, I'm going to divide by 0.3.
So 0.3/0.3 canceled.
S equals to $400.
So the regular selling price for the bike is $400.
Now look at the second question, B. During promotion, the bike was marked down for 25%.
What was the sale price?
So we know the amount of discount is 25% of the regular price.
So 25% of the regular price, which is $400.
That is $100.
So after offering discount of $100, also 25% off, the sale price is the regular selling
price subtract the amount of discount.
So it's $300.
Now we still need to find out what was the operating profit or loss during the promotion?
We'll use the same formula.
Selling price need used to cover cost and expenses and the profit.
The only difference now is, this selling price is sale selling price.
And the profit is profit during the sale.
So if this profit during sale is calculated to be negative, that means it's a loss.
If it's positive, of course, that's a profit.
So sale price, we know that's $300.
Cost stays the same.
$120.
Expenses.
So we know expenses were 40% of regular selling price.
So 40%, 0.4 times regular selling price.
And the profit during sale, that's unknown.
That's what we're looking for.
So profit during sale, we don't know.
Now in this equation, we only have one variable.
We'll move all the numbers to one side and then keep profit on the other side.
Positive 120 become negative.
The 0.4 times 400 is 160, move over to the left, so positive become negative.
And that is profit during the sale.
Okay, so we may also switch both sides.
Profit during sale equals to 300 minus 120 minus one 60 equals to $20.
So during the promotion, our profit is $20.
Now we solved the problem.
Thank you for watching.