Math Problem Statement

In order to make a profit, businesses must sell (mark up) their product for more than it costs to produce it. If the average production price for a certain product was $8.19, and they sold it for $13.99, by what percent was the product marked up?

Solution

To determine the percentage markup, you can use the following formula:

Markup Percentage=Selling PriceCost PriceCost Price×100\text{Markup Percentage} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100

Given:

  • Cost Price = $8.19
  • Selling Price = $13.99

Now, substitute the values into the formula:

Markup Percentage=13.998.198.19×100\text{Markup Percentage} = \frac{13.99 - 8.19}{8.19} \times 100

First, calculate the difference between the selling price and the cost price:

13.998.19=5.8013.99 - 8.19 = 5.80

Then, divide this difference by the cost price:

5.808.190.707\frac{5.80}{8.19} \approx 0.707

Finally, multiply by 100 to get the percentage:

0.707×100=70.7%0.707 \times 100 = 70.7\%

So, the product was marked up by approximately 70.7%.

Would you like further details on markup calculations or any other related topics?


Here are some follow-up questions for you:

  1. What would the selling price be if the markup was 50%?
  2. How would you calculate the profit margin on this product?
  3. How does a business determine the ideal markup percentage for its products?
  4. If the cost price increases to $9.50, what would the new markup percentage be?
  5. What is the difference between markup and profit margin?

Tip: Markup is based on the cost price, while profit margin is based on the selling price. Keep this in mind when comparing these metrics!

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Math Problem Analysis

Mathematical Concepts

Percentage
Markup Calculation

Formulas

Markup Percentage = ((Selling Price - Cost Price) / Cost Price) * 100

Theorems

Percentage Calculation

Suitable Grade Level

Grades 7-9