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Algebra / Linear inequalities in one or two variables Difficulty: Hard

A business owner plans to purchase the same model of chair for each of the $81$ employees. The total budget to spend on these chairs is $dollar sign 14,000$ , which includes a $7 percent sign$ sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?

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Explanation

Choice B is correct. It’s given that a business owner plans to purchase $81$ chairs. If $p$ is the price per chair, the total price of purchasing $81$ chairs is $81 p$ . It’s also given that $7 percent sign$ sales tax is included, which is equivalent to $81 p$ multiplied by $1.07$ , or $81 left parenthesis 1.07 right parenthesis p$ . Since the total budget is $dollar sign 14,000$ , the inequality representing the situation is given by $81 left parenthesis 1.07 right parenthesis p less than or equals 14,000$ . Dividing both sides of this inequality by $81 left parenthesis 1.07 right parenthesis$ and rounding the result to two decimal places gives $p less than or equals 161.53$ . To not exceed the budget, the maximum possible price per chair is $dollar sign 161.53$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the maximum possible price per chair including sales tax, not the maximum possible price per chair before sales tax.

Choice D is incorrect. This is the maximum possible price if the sales tax is added to the total budget, not the maximum possible price per chair before sales tax.