Robert has $50 to spend on his utility bills each month. The basic monthly charge for water and sewer is $23.77. Electricity costs $0.1116 for each kilowatt hour used. The inequality 0.1116x + 23.77 ? 50 represents Robert's monthly utility budget. To the nearest kilowatt hour, what is the maximum number of kilowatt hours of electricity that Robert can Use without going over his monthly budget amount?
Robert can use a maximum of 235 kilowatt hours of electricity without exceeding his monthly budget.
To determine the maximum kilowatt hours of electricity Robert can use within his budget, we need to solve the inequality \(0.1116x + 23.77 \leq 50\), which leads to a calculation resulting in approximately 235 kilowatt hours.
This option exceeds Robert's budget significantly. If he were to use 661 kilowatt hours, the total cost for electricity would be calculated as \(0.1116 \times 661 + 23.77\), which far surpasses $50, making this choice infeasible.
This choice correctly represents the maximum number of kilowatt hours Robert can use without exceeding his budget. By solving the inequality, we find that using 235 kilowatt hours maintains the total cost at exactly $50, thus adhering to his financial constraints.
Using 448 kilowatt hours would result in a total cost of \(0.1116 \times 448 + 23.77\), which exceeds $50. Therefore, this option is not viable as it surpasses Robert's monthly budget.
Similar to option C, using 424 kilowatt hours would also lead to a total cost of \(0.1116 \times 424 + 23.77\), which again exceeds the budget of $50. This makes it another incorrect choice.
Robert's monthly utility budget dictates that he can spend up to $50. By solving the inequality for electricity costs while accounting for the fixed charge, we find that the maximum kilowatt hours he can use is 235. This ensures he remains within his budget, whereas the other options result in exceeding the financial limit.
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