High School

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Write a complex percentage problem and outline the procedures for teaching students how to solve this type of problem.

Example Problem:
A store is having a sale with 25% off all items. If the original price of a jacket is $120 and a customer has a coupon for an additional 10% off the sale price, what is the final price the customer pays for the jacket?

Procedures for Teaching:

1. **Understanding the Problem:**
- Read the problem carefully.
- Identify the original price, the percentage of the sale discount, and the additional discount.

2. **Calculate the Sale Price:**
- Calculate the sale discount: Multiply the original price by 25% (0.25).
- Subtract the discount from the original price to find the sale price.

\[
\text{Sale Price} = \text{Original Price} - (\text{Original Price} \times 0.25)
\]

3. **Apply the Additional Discount:**
- Calculate the additional discount on the sale price: Multiply the sale price by 10% (0.10).
- Subtract the additional discount from the sale price to find the final price.

\[
\text{Final Price} = \text{Sale Price} - (\text{Sale Price} \times 0.10)
\]

4. **Verification:**
- Double-check the calculations.
- Ensure the final price makes sense in the context of the problem.

5. **Discussion:**
- Discuss the importance of understanding each step.
- Highlight common mistakes and how to avoid them.

Answer :

Final answer:

To complex percentage problem solving, calculate the initial percentage, determine the absolute change, adjust the total number, and then calculate the new percentage.

Explanation:

Let's create a complex percentage problem and then describe the steps to solve it. Problem: A closet contains 37 shirts, of which 9 are red. If a student gains 24% more red shirts, what will be the new total number of shirts and what will be the percentage of red shirts?

  1. Calculate the percentage of red shirts in the initial scenario. Set up the equivalent fractions: 9/37 = x/100. Cross multiply and solve for x to get the initial percentage of red shirts.
  2. Calculate the increase in red shirts. 24% of 9 red shirts is approximately 2 (always round to the nearest individual object).
  3. Add the new red shirts to the total shirts. The total will be 37 + 2 = 39.
  4. Re-calculate the percentage of red shirts. Now there are 11 red shirts and 39 shirts in total. Set the equivalent fractions: 11/39 = y/100. Solve for y and round as necessary.

Learn more about Percentage Problem Solving here:

brainly.com/question/32587109

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Rewritten by : Barada