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2.6 - Successive Discounts

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Understanding Successive Discounts

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Teacher
Teacher

Good morning, everyone! Today, we're diving into the world of successive discounts—an essential concept in commercial math!

Student 1
Student 1

What exactly is a successive discount?

Teacher
Teacher

Great question! Successive discounts mean applying one discount after another on an item. For example, if a shirt costs $100 and has a 10% discount followed by another 20%, we apply the second discount on the price after the first discount.

Student 2
Student 2

So how do we calculate the selling price with multiple discounts?

Teacher
Teacher

We use the formula S.P. = M.P. × (1 - d1/100) × (1 - d2/100). Here, M.P. is the marked price and d1 and d2 are the discount percentages.

Student 3
Student 3

Could we do an example together?

Teacher
Teacher

Absolutely! Let's say an item has a marked price of $200, and there are discounts of 15% and 25%. The selling price will be calculated as follows: S.P. = 200 × (1 - 0.15) × (1 - 0.25).

Student 4
Student 4

I see how that works!

Teacher
Teacher

To summarize, successive discounts are calculated on an adjusted price, leading to a lower final price than expected if a single discount were applied. Keep practicing using the formula!

Applying Successive Discounts

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Teacher
Teacher

Let's practice! If a television has a marked price of $450 with discounts of 10% and 5%, how would you find the selling price?

Student 1
Student 1

First, we calculate 10% off, which gives us $450 - $45, leaving $405.

Student 2
Student 2

Then we take 5% off of $405, which is $20.25, right?

Teacher
Teacher

Correct! So what’s the final selling price?

Student 3
Student 3

It’s $405 - $20.25, equaling $384.75!

Teacher
Teacher

Well done! Remember, understanding successive discounts helps in real-life situations, like shopping!

Real-life Applications of Successive Discounts

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Teacher
Teacher

Now, let’s talk about where we see successive discounts in real life. Can anyone give an example?

Student 4
Student 4

How about during holiday sales or clearance events?

Teacher
Teacher

Exactly! Retailers often advertise multiple discounts to encourage purchase. Knowing how to compute these helps consumers get the best deals.

Student 1
Student 1

I think I understand it better now!

Teacher
Teacher

Let’s summarize today's lesson: Successive discounts are sequential discounts applied to already discounted prices, often used in sales promotions.

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

Successive discounts involve applying multiple discounts sequentially to a marked price, leading to a modified selling price.

Standard

When more than one discount is offered on a product, successive discounts are calculated by applying each discount on the reduced price sequentially. This method affects the final selling price, which is derived from the marked price using a specific formula.

Detailed

Detailed Summary of Successive Discounts

Successive discounts occur when an item has multiple discounts applied consecutively rather than a single discount. This is commonplace in retail and sales promotions. The final selling price is calculated using the formula:

S.P. = M.P. × (1 - d1/100) × (1 - d2/100)

where M.P. is the marked price, and d1 and d2 are the successive discount percentages expressed in decimal form. This method ensures that subsequent discounts are calculated on the already discounted price, leading to a compounded effect that significantly alters the final selling price. Understanding how to compute successive discounts is essential for accurate pricing in commercial settings.

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Audio Book

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Understanding Successive Discounts

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When more than one discount is offered, each is applied on the reduced price.

Detailed Explanation

Successive discounts are discounts that are applied in sequence, meaning each discount is calculated on the price after the previous discount has been applied. For example, if an item has a marked price of $100 and you receive a 10% discount followed by another 20% discount, the second discount is applied to the new price after the first discount is taken into account, rather than the original price.

Examples & Analogies

Imagine you're buying a video game that's originally priced at $60. If there's a 40% discount followed by an additional 25% discount, the first discount reduces the price to $36. Then, applying the second discount, you would pay 25% of $36, which is $9 less, making the final price $27.

Calculating Net Selling Price

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Net Selling Price is calculated as: S.P. = M.P. × (1−d1/100) × (1−d2/100)

Detailed Explanation

The net selling price (S.P.) after applying successive discounts can be calculated using a specific formula. Here, M.P. stands for the marked price of the item, and d1 and d2 represent the first and second discount percentages, respectively. To find the net selling price, you first subtract the first discount percentage from 100%, multiply this decimal result by the marked price, and then take that new result and apply the second discount percentage using the same method.

Examples & Analogies

Let's say you have a shirt marked at $50. If there's a 10% discount followed by a 5% discount, you first calculate 10% of $50, which is $5. This gives a new price of $45. Next, take 5% of $45, which is $2.25. The final selling price will be $50 - $5 - $2.25 = $42.75.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Successive Discounts: Applying multiple discounts one after another to a product's price.

  • Marked Price (M.P.): The initial price before discounts are applied.

  • Selling Price (S.P.): The final price after all discounts have been taken into account.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Example: A marked price of $100 with a first discount of 20% and a second discount of 10%: S.P. = 100 × (1 - 0.20) × (1 - 0.10) = $72.

  • Example: If a jacket priced at $80 is discounted by 25% and then a further discount of 10% is applied: S.P. = 80 × (1 - 0.25) × (1 - 0.10) = $54.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • For discounts applied, step by step take a ride, reducing prices till you abide.

📖 Fascinating Stories

  • Imagine a shopper at a store finding a shirt for $100. First, there's a 10% discount which brings the price down to $90. Then, they find a 15% further discount, making the final price even sweeter at $76.50!

🧠 Other Memory Gems

  • Remember the formula with 'M.S.A.': Marked Price, Sequential Discounts, Achieve Selling Price!

🎯 Super Acronyms

Use 'D.S.S.' to recall

  • Discounts on Selling Stepwise.

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Marked Price (M.P.)

    Definition:

    The original price listed on the item before any discounts are applied.

  • Term: Selling Price (S.P.)

    Definition:

    The final price paid by the customer after applying all discounts.

  • Term: Successive Discounts

    Definition:

    Multiple discounts applied sequentially on an item's price.