https://file.aiquickdraw.com/mathbot/file/1728572891768gat9x4gx.jpg

The problem asks for equations that determine the total price $ y $, after a 7.5% sales tax is applied, where $ x $ represents the list price of the backpack.

### Step-by-step breakdown:
- Sales tax rate = 7.5%, or 0.075 as a decimal.
- The total price after tax includes both the original price and the tax.

The two correct equations are:
1. **$ y = 1.075x $** (Option B): This equation shows the total price $ y $ as 107.5% of the original price $ x $, which is the sum of the original price and the 7.5% tax.
2. **$ y = x + 0.075x $** (Option D): This equation expresses the total price as the original price plus the 7.5% tax, which is equivalent to $ y = 1.075x $.

### Incorrect Options:
- **$ y = 0.075x $** (Option A): This only gives the tax amount, not the total price.
- **$ y = 1.75x $** (Option C): This would imply a 75% tax, which is incorrect.
- **$ y = 0.75x $** (Option E): This would imply a reduction to 75% of the original price, which doesn't apply here.

Would you like further details or have any other questions?

### Related Questions:
1. What is the process for converting percentages to decimals?
2. How can you calculate sales tax for different percentages?
3. What does the term "list price" refer to in sales transactions?
4. How can we rewrite expressions like $ y = 1.075x $ in terms of components (price + tax)?
5. What would happen to the equation if the sales tax rate increased?

### Tip:
Always convert percentage rates to decimals by dividing by 100 when performing calculations 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? Select TWO correct answers.

Learn how to calculate the total price of an item after a 7.5% sales tax is applied. This problem involves key algebraic concepts, including the formulas y = 1.075x and y = x + 0.075x, to determine the total price. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation