Hai has $100 avialable to buy USB drives to back up data for him business computers. Each USB drive has a price of $8, and Hai will pay a sales tax of 7% of the total prices of the USB drives. What is the maximum number of USB drives Hai can buy?

Options

A. 11
B. 12
C. 13
D. 14

Answer

To find the maximum number of USB drives Hai can buy, we need to consider both the price of the USB drives and the sales tax applied to the total purchase. Here’s a step-by-step solution:

### Step 1: Define the variables
Let \( N \) be the number of USB drives Hai wants to buy. The price of one USB drive is $8.

### Step 2: Calculate the total price without tax
The total price for \( N \) USB drives is given by:
\[ \text{Total Price} = 8N \]

### Step 3: Calculate the sales tax
The sales tax is 7% of the total price. Therefore, the sales tax can be calculated as:
\[ \text{Sales Tax} = 0.07 \times (8N) = 0.56N \]

### Step 4: Write the total cost including tax
The total cost including the sales tax is:
\[ \text{Total Cost} = \text{Total Price} + \text{Sales Tax} = 8N + 0.56N = 8.56N \]

### Step 5: Set up the inequality
Since Hai has $100 available to spend, we set up the inequality:
\[ 8.56N \leq 100 \]

### Step 6: Solve for \( N \)
To find the maximum number of USB drives, we solve the inequality:
\[ N \leq \frac{100}{8.56} \]
Calculating the right side:
\[ N \leq 11.68 \]

### Step 7: Determine the maximum whole number of USB drives
Since \( N \) must be a whole number (you can't buy a fraction of a USB drive), we take the largest whole number less than or equal to 11.68, which is:
\[ N = 11 \]

### Conclusion
The maximum number of USB drives Hai can buy is **11**.

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