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?

Rationale

(100 - 35) / 20

To determine the greatest possible number of hours of labor Jordan can afford, we first subtract the fixed service fee of $35 from his total budget of $100, leaving him with $65 for labor. Dividing this amount by the hourly rate of $20 gives us the maximum hours of labor.

A ((100 - 35) / 20) CORRECT

This expression correctly calculates the number of hours of labor Jordan can afford after accounting for the service fee. Subtracting the service fee of $35 from the $100 budget results in $65, which when divided by the hourly rate of $20 gives 3.25 hours, the maximum hours available for labor without exceeding the budget.

B ((100 - 20) / 35) YOUR ANSWER

This option incorrectly subtracts the hourly rate of $20 from the total budget. It does not consider the service fee, leading to an inaccurate representation of the budget allocation for labor. The result will not provide the correct maximum hours of labor.

C (20 * (100 - 35)) YOUR ANSWER

This choice incorrectly multiplies the hourly rate by the remaining budget after the service fee. Instead of calculating the number of hours, it erroneously computes a dollar amount, which does not answer the question about the greatest number of labor hours.

D ((100 - 35) / (20 - 35)) YOUR ANSWER

This expression contains an incorrect denominator of (20 - 35), which results in a negative value and makes the calculation invalid. The negative value does not represent any feasible number of hours Jordan can afford for labor.

E (100 - 20 * 35) YOUR ANSWER

This choice incorrectly computes the budget by multiplying the hourly rate by the service fee. The operation does not account for the service fee correctly and results in a miscalculation of available funds for labor, leading to an illogical number.

Conclusion

The best representation of the greatest possible number of labor hours Jordan can afford is given by the expression (100 - 35) / 20. This calculation accurately considers the service fee, allowing for a correct determination of his remaining budget for labor, thereby ensuring that he does not exceed his total budget of $100.

(100 - 35) / 20

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