Question

URGENT Suppose that Student X wants to price items in their online store in such a way if they later go on sale for 25% off, Student X will still make a 20% profit over what they paid for the item. What should the original markup be for each item?

Answer 1

Explanation:

To determine the original markup for each item, we can use the information provided.

Let's assume the cost price of an item is represented by C. The goal is to set a selling price that, when later discounted by 25%, will still yield a 20% profit over the cost price.

First, let's calculate the selling price after the 25% discount. We can express it as 0.75 times the original selling price.

Next, we need to calculate the desired profit, which is 20% of the cost price. This can be expressed as 0.20 times the cost price.

To find the original markup, we need to set up the equation:

Selling price - 25% of the selling price = Cost price + Desired profit

Let's represent the selling price as S. Plugging in the values, we have:

S - 0.25S = C + 0.20C

Simplifying the equation, we get:

0.75S = 1.20C

To find the original markup, we need to express S in terms of C:

S = (1.20C) / 0.75

Simplifying further:

S = 1.6C

Therefore, the original markup should be 1.6 times the cost price of each item.

In summary, to ensure a 20% profit over the cost price when applying a 25% discount, Student X should set the original markup for each item at 1.6 times the cost price.