Question

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

Answer 1

To find the maximum price of a shirt that Alec can buy, we need to subtract the entrance fee and the sales tax from his budget. The greatest possible price of a shirt that would allow Alec to buy the shirts is approximately $8.70.

Step-by-step explanation:

To find the maximum price of a shirt that Alec can buy, we need to subtract the entrance fee and the sales tax from his budget.

Let's assume the price of each shirt is $x.

So, the total cost of 14 shirts without sales tax is 14x.

The total cost with sales tax is 14x + 0.05(14x).

Alec's budget is $130, but he also needs to pay the $2 entrance fee. So, we can set up the following equation: 130 - 2 = 14x + 0.05(14x).

Simplifying this equation, we get 128 = 14x(1 + 0.05).

We can solve this equation to find the value of x and determine the maximum price of a shirt that Alec can buy.

128 = 14x(1.05)

128 = 14.7x

x = 128 / 14.7

x ≈ 8.7046

Therefore, the greatest possible price of a shirt that would allow Alec to buy the shirts is approximately $8.70.