Final answer:
By converting both the Euros and Turkish lira spent during the layover and in Turkey to U.S. dollars using the provided exchange rates and subtracting from the initial $500, we arrive at a remaining amount of $176.73, which does not match any of the provided multiple-choice options.
Step-by-step explanation:
To determine the amount of U.S. dollars remaining after the described transactions, we need to convert the expenses into U.S. dollars using the provided exchange rates, and then subtract these expenses from the initial amount.
First, spending 150 Euros at duty-free during the layover in Italy, we convert this expense using the exchange rate of 0.88€ for $1.00 U.S. Hence,
150€ * (1 U.S. dollar / 0.88€) = $170.45.
In Turkey, you spend 433 Turkish lira (TRY) on food. Using the exchange rate of 3.22 TRY for 1€: 433 TRY / 3.22 TRY = 134.47€. Then, converting into U.S. dollars: 134.47€ * (1 U.S. dollar / 0.88€) = $152.80.
Lastly, we subtract the total expenses in U.S. dollars from the starting amount:
$500 - $170.45 - $152.80 = $176.75.
However, since this final amount is not one of the provided options (A) $349.28 (B) $359.62 (C) $369.94 (D) $380.26, it appears there may have been a miscalculation. Let's retry the calculations with more precision:
150€ / 0.88€ = $170.4545
433 TRY / 3.22 TRY = 134.47€
134.47€ / 0.88€ = $152.81
Now the subtraction gives a more precise result:
$500 - $170.4545 - $152.81 = $176.7345.
Round this amount to two decimal places, and you get $176.73, which still does not correspond to any of the provided options. Therefore, it's important to double-check the calculation steps and also verify if the provided options are correct. In this case, I would double-check the exchange rates and expenses, as the given options may imply a different rate or amount spent.