To determine which situation is best represented by the equation \( 68.50x + 127.95 = 675.95 \), we need to analyze each option and see how it fits the equation.
Let's break down the equation:
- \( 68.50x \): This term represents a variable cost that depends on the number of hours (or items) worked (or purchased), represented by \( x \).
- \( 127.95 \): This is a fixed cost (a cost not depending on \( x \)).
- \( 675.95 \): This is the total cost that combines both fixed and variable costs.
Now let's go through each option:
Option A:
- An office manager paid \( 675.95 \) to build a website.
- The office manager bought a software package for \( 68.50 \) (which would represent a one-time purchase).
- The employee is paid \( 127.95 \) per hour worked.
The last statement should read "paid an employee \( 127.95 \) per hour". In this case, plugging \( x \) as the number of hours worked gives us:
\[ 68.50(1) + 127.95x = 675.95 \]
This does not match \( 68.50x + 127.95 = 675.95 \) directly because we wouldn’t have \( x \) in the first term. This option is not represented by the equation.
Option B:
- The office manager paid \( 675.95 \) for computer equipment.
- The office manager bought one monitor for \( 127.95 \).
- Hard drives are \( 68.50 \) each.
The equation would represent buying \( x \) hard drives:
\[ 68.50x + 127.95 = 675.95 \]
This matches our equation perfectly. Therefore, Option B is represented by the equation.
Option C:
- The sales manager paid \( 675.95 \) for advertising.
- The sales manager paid \( 127.95 \) per hour for consulting.
- Received a discount of \( 68.50 \).
This is confusing because the received discount does not fit well in the equation structure \( 68.50x + 127.95 = 675.95 \). Here, the costs would be added or subtracted differently. Thus, Option C is not represented by the equation.
Option D:
- A business owner paid a total of \( 675.95 \) for two employees.
- One employee is paid \( 68.50 \) (which could imply \( x \) days or some variable).
- The second employee is paid \( 127.95 \) per day.
If we interpret this as two different wages per day for \( x \) days of work, it won't align because \( 68.50x + 127.95 = 675.95 \) would require a different interpretation of how to sum the payments. This also does not represent the proper use of \( x \).
Conclusion:
The only option that directly matches the equation \( 68.50x + 127.95 = 675.95 \) is Option B.
Thus, the correct answer is: B: An office manager paid $675.95 for computer equipment. The office manager bought one monitor for $127.95 and hard drives for $68.50 each. What is \( x \), the number of hard drives the office manager bought?
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