Lucky you! You went to couponcabin.com and found a 20% off coupon to your partner’s favorite store. Armed with that coupon, you went to the store only to find a storewide sale offering 10% off everything in the store. In addition, your credit card has a special offer that allows you to save 10% if you use your credit card for all purchases that day. Using your credit card, what will you pay before tax for the $155 gift you found? Use the single equivalent discount to calculate how much you save and then calculate your final price.

To solve this, we need to find the single equivalent discount by combining the three successive discounts: 20% from the coupon, 10% from the storewide sale, and 10% from the credit card offer. Successive discounts multiply together to give the equivalent total discount.

The general formula for calculating the final price after successive discounts is:

\[
\text{Final Price} = P \times (1 - d_1) \times (1 - d_2) \times (1 - d_3)
\]

where:
- $P$ is the original price,
- $d_1$, $d_2$, and $d_3$ are the discount percentages expressed as decimals.

For this problem:
- $P = 155$,
- $d_1 = 0.20$ (20% off coupon),
- $d_2 = 0.10$ (10% storewide sale),
- $d_3 = 0.10$ (10% credit card offer).

### Step 1: Calculate the final price using successive discounts
\[
\text{Final Price} = 155 \times (1 - 0.20) \times (1 - 0.10) \times (1 - 0.10)
\]
\[
\text{Final Price} = 155 \times 0.80 \times 0.90 \times 0.90
\]
\[
\text{Final Price} = 155 \times 0.648
\]
\[
\text{Final Price} \approx 100.44
\]

### Step 2: Calculate the amount saved
The amount saved is the difference between the original price and the final price:

\[
\text{Amount Saved} = 155 - 100.44 = 54.56
\]

### Final Answer:
- The final price before tax is **$100.44**.
- The total amount saved is **$54.56**.

Would you like further details or explanations on any of the steps?

Here are 5 related questions for further exploration:
1. How would the result change if there were an additional 5% discount applied at the end?
2. What is the general formula for combining successive discounts?
3. How does applying discounts successively differ from adding discount percentages directly?
4. How would the final price change if the original price was $200 instead of $155?
5. Can you always multiply successive discount percentages to get the total discount?

**Tip:** Successive discounts are always multiplied, not added, to account for the fact that each discount is applied to a reduced price.

Learn how to calculate the final price of a $155 gift using successive discounts of 20%, 10%, and 10%. This problem covers key concepts like percentage discounts and algebraic methods to combine multiple discounts. Suitable for students in Grades 8-10.

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