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The problem involves calculating the total price of a backpack after adding a 7.5% sales tax. The given list price is $54. The goal is to select two correct equations where $ y $ represents the total price after tax, and $ x $ is the list price.

### Let's break down the problem:
1. **Sales Tax Rate**: 7.5% or $ 0.075 $ as a decimal.
2. **Formula for Total Price**: The total price, $ y $, is calculated as:
   \[
   y = x + 0.075x = (1 + 0.075)x = 1.075x
   \]
   This equation shows that the total price is 107.5% of the list price.

### Analyze the options:
- **A**: $ y = 0.075x $ – This equation only represents the tax amount, not the total price.
- **B**: $ y = 1.075x $ – This is correct, as it represents the total price including the tax.
- **C**: $ y = 1.75x $ – This equation suggests a 75% tax, which is incorrect.
- **D**: $ y = x + 0.075x $ – This is correct, as it shows the original price plus the tax.
- **E**: $ y = 0.75x $ – This represents a 75% discount, not the total price after adding tax.

### Correct answers:
- **B**: $ y = 1.075x $
- **D**: $ y = x + 0.075x $

Would you like further details on how the tax is applied or help with another question?

### 5 Related Questions:
1. What is the equation if the tax rate was 10% instead of 7.5%?
2. How do you find the sales tax amount alone from the total price?
3. How would you calculate the price after a 20% discount followed by a 7.5% tax?
4. What would be the total price if there was no sales tax?
5. How would the equations change if the price of the backpack increased by 15%?

**Tip**: Always convert percentage rates into decimals when using them in equations!

The list price of a backpack is $54.00, and the store applies a 7.5% sales tax. Which equations can be used to determine the total price, y, after sales tax, where x represents the list price of the backpack?

Learn how to calculate the total price of a backpack with a 7.5% sales tax. This problem covers essential concepts like sales tax calculation and forming algebraic equations for students in Grade 7.

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