Let’s analyze this question step by step.

Problem Overview:

Leila is buying a model that costs $x$ dollars. In addition to the price, she has to pay a 7% tax. We need to find expressions that represent the total amount Leila pays, including the tax.

Breakdown:

1. 7% tax means Leila pays an additional $7\%$ of $x$, which is: $0.07x$

2. The total payment is the price of the model plus the tax: $x + 0.07x$

3. Factoring $x$: $x(1 + 0.07) = 1.07x$

Thus, the total can be expressed as $x + 0.07x$ or $1.07x$.

Answer Choices:

1. Option A: $\frac{107}{100}x$
   $\frac{107}{100} = 1.07$ This matches $1.07x$, so it is correct.

2. Option B: $0.7x + x$
   This is incorrect because $0.7x + x = 1.7x$, which is not what the total should be.

3. Option C: $1.07x$
   This directly represents the total, so it is correct.

4. Option D: $x + \frac{7}{10}$
   This is incorrect because $\frac{7}{10}$ is not the same as $7\%$ of $x$, and the addition is not calculated correctly.

Final Answer:

The two correct expressions are:

• Option A: $\frac{107}{100}x$
• Option C: $1.07x$

Would you like a deeper explanation of any part of this?

Follow-up Questions:

1. What is the process for converting percentages to decimals?
2. How do you factor expressions like $x + 0.07x$?
3. Can you generalize the formula for adding tax to a price?
4. Why is $0.7x + x$ not correct in this case?
5. How does simplifying fractions like $\frac{107}{100}$ work?

Tip:

Always verify the meaning of percentages in word