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Alec must purchase 14 identical shirts and only has $130. There is a flat $2 entrance fee for shopping at the warehouse store where he plans to buy the shirts. The price of each shirt is the same whole-dollar amount. Assuming a 5% sales tax is added to the price of each shirt, what is the greatest possible price (in dollars) of a shirt that would allow Alec to buy the shirts?

 Oct 19, 2019
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$130 - $2 = $128 that Alex has left for 14 shirts.

 

Let the price of each shirt =P

 

1.05P x 14 = 128

 

14.7P = 128      Divide both sides by 14.7

 

P = 128 / 14.7

 

P = $8.71 - price of a shirt. But, since the price of a shirt is a "whole number", then it would have to be "rounded down" in order for Alex to be able to buy 14 shirts. In other words, the greatest possible price would have to be $8 per shirt, because: $8 x 1.05 (sales tax) x 14 shirts =$117.60. If the price of the shirt was "rounded up" to $9 per shirt, then: $9 x 1.05 x 14 =$132.30 which Alex couldn't afford.

 Oct 19, 2019

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