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?

Select TWO correct answers.
A.y= 0.075x
B.y= 1.075x
C.y= 1.75x
D.y= x + 0.075x
E.y= 0.75x

To determine the total price after applying a 7.5% sales tax, let's analyze the situation step by step.

- **The list price of the backpack** is $ x = 54 \, \text{dollars} $.
- **Sales tax** is 7.5%, which means 7.5% of the list price will be added to the total price.

### Approach:

1. The sales tax amount is $ 0.075x $ (since 7.5% = $ 7.5/100 = 0.075 $).
2. The total price after tax is the list price plus the sales tax amount:
   \[
   \text{Total Price} = x + 0.075x
   \]
   Factoring out $ x $, this can be written as:
   \[
   \text{Total Price} = x(1 + 0.075) = 1.075x
   \]

### Correct Equations:

- **Option B:** $ y = 1.075x $ is correct because it shows the total price as 1.075 times the list price.
- **Option D:** $ y = x + 0.075x $ is correct because it represents the sum of the list price and the sales tax.

### Incorrect Options:

- **Option A:** $ y = 0.075x $ is incorrect because it only represents the sales tax amount, not the total price.
- **Option C:** $ y = 1.75x $ is incorrect because it mistakenly suggests a 75% tax.
- **Option E:** $ y = 0.75x $ is incorrect because it suggests a 75% reduction, not an increase.

### Summary:

The two correct equations are:
- **B:** $ y = 1.075x $
- **D:** $ y = x + 0.075x $

Would you like more details or have any questions?

### Follow-up questions:
1. What is the total price of the backpack if the list price is $54.00?
2. How would the equation change if the sales tax were 10% instead?
3. Can the percentage increase be written as a fraction? If so, what would it be for 7.5%?
4. What would happen to the equation if the store applied a discount instead of a tax?
5. How do you calculate the amount of sales tax alone if you know the total price?

### Tip:
Always remember that when dealing with percentages, converting the percentage to a decimal (by dividing by 100) is essential to perform calculations correctly.

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? Select TWO correct answers. A.y= 0.075x B.y= 1.075x C.y= 1.75x D.y= x + 0.075x E.y= 0.75x

Learn how to calculate the total price of a backpack after applying a 7.5% sales tax. This problem covers essential algebraic concepts and percentage calculations. Ideal for students in Grades 6-8, it demonstrates the correct equations to use when determining the final price with sales tax.

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