Iris's assumption that applying a 10% discount followed by a 20% discount is equivalent to a 30% discount is incorrect. Let's break down the calculation to see why.

Step-by-Step Calculation:

1. Initial Price: $260.

2. First Discount (10%): $\text{Discount amount} = 0.10 \times 260 = 26$ \text{Price after 10% discount} = 260 - 26 = 234

3. Second Discount (20% applied on the discounted price of $234): $\text{Discount amount} = 0.20 \times 234 = 46.8$ $\text{Final Price after both discounts} = 234 - 46.8 = 187.20$

Comparison to Assumed Price:

Iris assumed that applying a combined 30% discount directly to the original price would result in:

$\text{Assumed Price} = 260 \times (1 - 0.30) = 260 \times 0.70 = 182$

Conclusion:

• Final Price with Sequential Discounts: $187.20
• Assumed Price with a 30% Direct Discount: $182

Explanation: Applying sequential discounts (10% followed by 20%) does not equal a simple 30% discount because the second discount is applied to a reduced price, not the original price.

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Would you like further clarification or have any questions? Here are some related questions you might consider:

1. How do compound discounts differ from single equivalent discounts?
2. Can you find the equivalent single discount for sequential discounts of 10% and 20%?
3. How do you calculate the final price with multiple discounts?
4. What is the formula for combining two sequential discounts?
5. How can this mistake in assumptions be avoided in future shopping?

Tip: When dealing with multiple discounts, always apply them sequentially rather than combining them into one percentage to avoid incorrect assumptions.