Let's break down the problem and solve it step by step.

Problem Details:

• Regular price of the shoes: $129
• Discount: 24% off
• Sales tax: 6.4%

Step 1: Find the price after discount

First, calculate the amount of the discount.

$\text{Discount} = 24\% \times 129 = 0.24 \times 129 = 30.96$

Now, subtract the discount from the regular price to find the sale price.

$\text{Sale Price} = 129 - 30.96 = 98.04$

Step 2: Calculate the sales tax

Now, calculate the sales tax on the sale price.

$\text{Sales Tax} = 6.4\% \times 98.04 = 0.064 \times 98.04 = 6.27$

Step 3: Calculate the total price

Finally, add the sales tax to the sale price to find the total amount Zach will pay.

$\text{Total Price} = 98.04 + 6.27 = 104.31$

Final Answer:

Zach will pay $104.31 in total after the discount and sales tax.

Let me know if you need further explanation or details! Here are a few related questions to help explore the topic further:

1. How would the final price change if the discount was 30% instead of 24%?
2. How can we calculate a price with multiple discounts in a series?
3. What is the formula for calculating the final price after tax and discount?
4. How does compound tax work if there is a secondary tax after the first one is applied?
5. How would the sales tax affect the price if the shoes cost $150 instead of $129?

Tip: To easily calculate a price after a discount and tax, you can use this formula: $\text{Final Price} = \left( \text{Original Price} - \text{Discount} \right) \times (1 + \text{Sales Tax})$