Question

A2: A pool contractor can spend at most $425 a day on operating costs and payroll. It costs $75 each day to operate the excavator and $50 a day for each crew member. Write an inequality to represent the contractor's budget for the day.

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0 ≤ 50x + 75 ≤ 425
0 ≥ 50 − 75x ≥ 425
0 ≥ 50x + 75 ≥ 425
0 ≤ 50 − 75x ≤ 425

Answer 1

The correct inequality to represent the contractor's budget for the day is 0 ≤ 50x + 75 ≤ 425.

Explanation:

This inequality states that the total operating cost, which is equal to $50C + $75E (where C is the number of crew members and E is the number of days the excavator is used), must be greater than or equal to 0 and less than or equal to $425. This accurately represents the contractor's budget constraints, as the total operating cost cannot be negative and must be less than or equal to the maximum amount the contractor can spend.

The other inequalities listed in the question do not accurately represent the contractor's budget constraints. For example, the inequality 0 ≥ 50 − 75x ≥ 425 states that the total operating cost must be greater than or equal to 0 and less than or equal to $425, but it does not include the term for the cost of operating the excavator. Therefore, it does not accurately represent the budget constraints of the contractor.