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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) 
12 h-37 >= 86
(B) 
12(h-37) >= 86
(c) 
12 h+37 >= 86
(D) 
12(h+37) >= 86

A barber charges $12 \$ 12 for a haircut. His \mathrm{His} operating expenses are, on average, $37 \$ 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 \$ 86 . If the barber gives h h haircuts in a day, which inequality best models this situation?\newlineChoose 11 answer:\newline(A) 12h3786 12 h-37 \geq 86 \newline(B) 12(h37)86 12(h-37) \geq 86 \newline(C) 12h+3786 12 h+37 \geq 86 \newline(D) 12(h+37)86 12(h+37) \geq 86

Full solution

Q. A barber charges $12 \$ 12 for a haircut. His \mathrm{His} operating expenses are, on average, $37 \$ 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 \$ 86 . If the barber gives h h haircuts in a day, which inequality best models this situation?\newlineChoose 11 answer:\newline(A) 12h3786 12 h-37 \geq 86 \newline(B) 12(h37)86 12(h-37) \geq 86 \newline(C) 12h+3786 12 h+37 \geq 86 \newline(D) 12(h+37)86 12(h+37) \geq 86
  1. Define Variables and Situation: Define the variables and the situation.\newlineThe barber charges $12\$12 per haircut and has operating expenses of $37\$37 per day. He wants to make at least $86\$86 profit in a day. Let hh represent the number of haircuts the barber gives in a day.
  2. Calculate Daily Earnings: Write an expression for the barber's daily earnings from haircuts. The barber earns $12\$12 for each haircut, so his earnings from hh haircuts would be 12h12h dollars.
  3. Calculate Profit: Write an expression for the barber's profit.\newlineThe barber's profit is his earnings minus his operating expenses. So, the profit PP can be expressed as P=12h37P = 12h - 37.
  4. Set Profit Goal: Write an inequality to represent the barber's goal for profit. The barber wants to make at least $86\$86 profit, so the inequality should reflect that his profit PP should be greater than or equal to 8686. Therefore, the inequality is 12h378612h - 37 \geq 86.
  5. Match Inequality to Choices: Match the inequality to the given choices.\newlineThe inequality we derived is 12h378612h - 37 \geq 86, which matches choice (A)(A).

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