Math Problem Statement

The selling price of an item is $520. It is marked down by 10%, but this sale price is still marked up from the cost of $360. Find the markup from cost to sale price.

Solution

The problem in the image states:

  • Selling price: $520
  • Marked down by: 10%
  • Cost: $360
  • Objective: Find the markup from the cost to the sale price.

Let's go through the solution again to ensure accuracy.

Step 1: Understand the Discounted Price and Original Price

Since the item was marked down by 10%, the sale price of $520 represents 90% of the original price. Let’s call the original price PP.

0.9×P=5200.9 \times P = 520 Solving for PP: P=5200.9=577.78P = \frac{520}{0.9} = 577.78

So, the original price was approximately $577.78 before the markdown.

Step 2: Calculate the Markup from Cost to Sale Price

Markup is found by comparing the sale price to the original cost:

Markup=520360=160\text{Markup} = 520 - 360 = 160

Final Answer:

The markup is $160.

Let me know if you have any questions or need additional details!


Here are some related questions for further practice:

  1. How would you find the markup percentage based on the cost price?
  2. If the markup percentage was instead 25% on the cost, what would be the sale price?
  3. How does a markdown affect profit when there is already a markup on the item?
  4. How would you calculate the original price if only the sale price and markdown percentage were known?
  5. What would happen to the sale price if the item were marked down by 20% instead of 10%?

Tip: Markup calculations can vary depending on whether they are based on cost or sale price, so double-check the base value in such problems.

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Math Problem Analysis

Mathematical Concepts

Percentage
Markup Calculation
Discount

Formulas

Original Price Calculation: 0.9 * Original Price = Sale Price
Markup Calculation: Sale Price - Cost

Theorems

Percentage theorem

Suitable Grade Level

Grades 7-8