We are currently studying "earning money" for math. I read this sentence:

When a store claculates its profit as a percentage of its cost price the profit is always bigger than the profit calculated as a percentage of the selling price.

What does it mean and please give me an example.

Thank you :)

cost: $10

selling price: $15
profit: $5

profit/cost = 5/10 = 50%
profit/sellprice = 5/15 = 33%

assuming s > c
ps > pc
divide by sc:
p/c > p/s

The sentence you mentioned states that when a store calculates its profit as a percentage of the cost price, the resulting profit is always greater than if it were calculated as a percentage of the selling price.

To understand this, let's define a few terms first:

1. Cost price: The amount of money a store spends to acquire or produce an item.
2. Selling price: The price at which the store sells the item.
3. Profit: The difference between the selling price and the cost price.

Now, let's consider an example to illustrate this concept:

Suppose a store buys a shirt from a wholesaler for $20 (cost price) and sells it to a customer for $30 (selling price). To calculate the profit as a percentage of the cost price, we need to find the difference between the selling price and the cost price:

Profit = Selling price - Cost price
Profit = $30 - $20
Profit = $10

To find the profit as a percentage of the cost price, we divide the profit by the cost price and multiply by 100:

Profit percentage (based on cost price) = (Profit / Cost price) * 100
Profit percentage (based on cost price) = (10 / 20) * 100
Profit percentage (based on cost price) = 50%

Now, let's calculate the profit as a percentage of the selling price:

Profit percentage (based on selling price) = (Profit / Selling price) * 100
Profit percentage (based on selling price) = (10 / 30) * 100
Profit percentage (based on selling price) = 33.33%

As you can see, the profit calculated as a percentage of the cost price is 50%, while the profit calculated as a percentage of the selling price is 33.33%. Therefore, in this example, the profit calculated as a percentage of the cost price is greater than the profit calculated as a percentage of the selling price, supporting the statement mentioned in the question.

It is important to note that this statement holds true in most cases, but it may not always be the case, especially in situations where the selling price is significantly higher than the cost price.