25. Jordan has budgeted $100 for the repair of his computer. The repair service charges a service fee of $35 for each repair job plus $20 per hour of labor. Which of the following represents the greatest possible number of hours of labor that the repair service can charge at that rate without exceeding Jordan's budget?
Answer: A
The greatest possible number of hours of labor that can be charged is represented by (100 - 35) / 20.
To determine the maximum number of hours of labor Jordan can afford, we first subtract the fixed service fee of $35 from his total budget of $100. This leaves him with $65, which he can then divide by the hourly labor cost of $20.
A) (100 - 35) / 20
This option correctly calculates the maximum hours of labor Jordan can afford. By subtracting the service fee of $35 from the budget of $100, we get $65, which, when divided by the hourly rate of $20, gives the number of hours he can afford.
B) (100 - 20) / 35
Option B incorrectly subtracts the hourly labor cost of $20 from the total budget. This calculation does not consider the fixed service fee, making it inaccurate for determining the number of hours of labor that can be charged.
C) 20 * (100 - 35)
This option multiplies the remaining budget after the service fee by the hourly rate, which is not a valid approach for finding the number of hours. Instead of calculating hours, it results in a total dollar amount, thereby failing to answer the original question.
D) (100 - 35) / (20 - 35)
Option D has a division by a negative number, which is mathematically incorrect in this context. The calculation does not reflect the relationship between the budget, service fee, and labor cost, and therefore is not useful for determining the maximum labor hours.
E) 100 - 20 * 35
This option incorrectly calculates a total amount by subtracting the product of the hourly rate and an arbitrary number from the total budget. It does not relate to the task of determining how many hours of labor can be afforded after accounting for the service fee.
Conclusion
Option A is definitively correct as it accurately reflects the budget allocation for labor after accounting for the service fee, resulting in the proper calculation of hours of labor. All other options fail to correctly relate the budget constraints to the cost structure, either through incorrect arithmetic or misunderstanding of the problem.