Question

Is a $10 \%$ discount followed by a $30 \%$ discount the same as a $30 \%$ discount followed by a $10 \%$ discount? Justify your answer.

Name: Problem 52, Chapter 2: Intermediate Algebra
Uploaded: 2022-02-25T22:01:27-08:00
Duration: 1 min 22 s
Channel: Victor Salazar
Description: Is a 10 % discount followed by a 30 % discount the same as a 30 % discount followed by a 10 % discount? Justify your answer.

   Is a $10 \%$ discount followed by a $30 \%$ discount the same as a $30 \%$ discount followed by a $10 \%$ discount? Justify your answer.

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 2, Problem 52

Instant Answer

Solved by Expert Victor Salazar

02/25/2022

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Step 1: Let's assume we have an item that costs $1. Show more…

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Is a $10 \%$ discount followed by a $30 \%$ discount the same as a $30 \%$ discount followed by a $10 \%$ discount? Justify your answer.

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Key Concepts

Commutativity of Multiplication

The commutative property of multiplication states that the order in which factors are multiplied does not affect the product. Since successive discounts are represented as multiplicative factors, their order does not change the final result.

Effective Discount Calculation

Effective discount calculation involves multiplying the complementary factors of the individual discounts (for example, 0.9 for 10% and 0.7 for 30%). The final price is given by multiplying these factors with the original price, demonstrating that the overall discount is identical regardless of the order in which the discounts are applied.

Successive Discounts

Successive discounts involve applying one percentage reduction after another on a base value. Each discount is applied to the remaining amount after the previous discount, which means the discounts compound multiplicatively rather than simply adding together.

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