A store has a sale with 40% off every item when you enter the store you receive a coupon that states that you receive an additional 10% off is this equal to a 50% percent discount? 

No, a 40% discount followed by an additional 10% discount is not the same as a 50% discount. This is because the second discount is applied to the already reduced price, not the original price.

Here's how you can calculate it:

1. **Start with the original price $ P $.**
2. **First discount:** Apply the 40% discount.
   \[
   \text{Price after 40% discount} = P - 0.4P = 0.6P
   \]

3. **Second discount:** Apply the additional 10% discount to the new price.
   \[
   \text{Price after additional 10% discount} = 0.6P - 0.1 \times 0.6P = 0.6P \times 0.9 = 0.54P
   \]

So, the final price is 54% of the original price, which means the total discount is:

\[
100\% - 54\% = 46\%
\]

Therefore, the total discount is **46%**, not 50%.

Would you like more details or have any questions? Here are some related questions:

1. What would the final price be if the original price is $100?
2. How would the total discount change if the additional discount was 20% instead of 10%?
3. If the store offered a 50% discount instead of the combined 40% and 10%, what would be the price difference?
4. How would the discount calculation change if the order of the discounts were reversed?
5. What is the equivalent single discount percentage for a 40% discount followed by a 20% discount?

**Tip:** When multiple percentage discounts are applied sequentially, the total discount is not simply the sum of the percentages; it's a cumulative effect, which is less than the sum.

Explore how sequential percentage discounts work with a detailed explanation on how a 40% discount followed by an additional 10% discount does not equal a 50% discount. Learn the step-by-step calculation method and understand the cumulative effect of discounts on the final price. Suitable for high school students and anyone interested in understanding discount calculations.

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