A pair of tennis shoes cost $48.60 including sales tax. If she sales tax rate is 8%, what is the cost of the tennis shoes before the tax is added?

Options

A. 10
B. 30
C. 40
D. 45

Answer

To find the cost of the tennis shoes before tax, we can follow these steps:

### Step 1: Understand the relationship between cost and tax
Let \( X \) be the cost of the tennis shoes before tax. The sales tax is 8% of this cost.

### Step 2: Calculate the sales tax
The sales tax can be expressed as:
\[ \text{Sales Tax} = \frac{8}{100} \times X = \frac{8X}{100} \]

### Step 3: Set up the equation for the total cost
The total cost of the shoes including tax is given as $48.60. Therefore, we can write the equation:
\[ X + \frac{8X}{100} = 48.60 \]

### Step 4: Combine like terms
To combine the terms on the left side, we can express \( X \) as \( \frac{100X}{100} \):
\[ \frac{100X}{100} + \frac{8X}{100} = 48.60 \]
This simplifies to:
\[ \frac{108X}{100} = 48.60 \]

### Step 5: Solve for \( X \)
To isolate \( X \), multiply both sides by 100:
\[ 108X = 48.60 \times 100 \]
Calculating the right side:
\[ 108X = 4860 \]
Now, divide both sides by 108:
\[ X = \frac{4860}{108} \]

### Step 6: Calculate the value of \( X \)
Now, we perform the division:
\[ X = 45 \]

### Conclusion
The cost of the tennis shoes before tax is:
\[ \boxed{45} \]

---