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Linear inequalities in one or two variables SAT question
Math · Algebra · Hard · Answer it here, explanation included.
A business owner plans to purchase the same model of chair for each of the employees. The total budget to spend on these chairs is , which includes a 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?
ExplanationShow
Choice B is correct. It’s given that a business owner plans to purchase chairs. If is the price per chair, the total price of purchasing chairs is . It’s also given that sales tax is included, which is equivalent to multiplied by , or . Since the total budget is , the inequality representing the situation is given by . Dividing both sides of this inequality by and rounding the result to two decimal places gives . To not exceed the budget, the maximum possible price per chair is .
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.
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