A barber charges $12 for a haircut. His operating expenses are, on average, $37 per day. He calculates his profit by subtracting his operating costs from the money he earns from the haircuts he gives. In a given day, the barber expects to make a profit of at least $86. If the barber gives h haircuts in a day, which inequality best models this situation?Choose 1 answer:(A) 12h−37≥86(B) 12(h−37)≥86(C) 12h+37≥86(D) 12(h+37)≥86
Q. A barber charges $12 for a haircut. His operating expenses are, on average, $37 per day. He calculates his profit by subtracting his operating costs from the money he earns from the haircuts he gives. In a given day, the barber expects to make a profit of at least $86. If the barber gives h haircuts in a day, which inequality best models this situation?Choose 1 answer:(A) 12h−37≥86(B) 12(h−37)≥86(C) 12h+37≥86(D) 12(h+37)≥86
Define Variables and Situation: Define the variables and the situation.The barber charges $12 per haircut and has operating expenses of $37 per day. He wants to make at least $86 profit in a day. Let h represent the number of haircuts the barber gives in a day.
Calculate Daily Earnings: Write an expression for the barber's daily earnings from haircuts. The barber earns $12 for each haircut, so his earnings from h haircuts would be 12h dollars.
Calculate Profit: Write an expression for the barber's profit.The barber's profit is his earnings minus his operating expenses. So, the profit P can be expressed as P=12h−37.
Set Profit Goal: Write an inequality to represent the barber's goal for profit. The barber wants to make at least $86 profit, so the inequality should reflect that his profit P should be greater than or equal to 86. Therefore, the inequality is 12h−37≥86.
Match Inequality to Choices: Match the inequality to the given choices.The inequality we derived is 12h−37≥86, which matches choice (A).
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