while traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after…

while traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent. 1 european euro = 1.3687 us dollars\n44.70 us dollars\n73.06 us dollars\n136.87 us dollars\n140.41 us dollars

while traveling to europe, phelan exchanged 250 us dollars for euros. he spent 150 euros on his trip. after returning to the united states he converts his money back to us dollars. how much of the original 250 us dollars does phelan now have? round to the nearest cent. 1 european euro = 1.3687 us dollars\n44.70 us dollars\n73.06 us dollars\n136.87 us dollars\n140.41 us dollars

Answer

Answer:

D. 140.41 US dollars

Explanation:

Step1: Calculate euros left

Phelan started with 250 US - dollars worth of euros. He spent 150 euros. First, find out how many euros he has left. He started with $\frac{250}{1.3687}$ euros (since 1 euro = 1.3687 US - dollars), but we can also just work with the euros he has left after spending. He has $250\div1.3687 - 150$ euros left. But a simpler way is to note that he spent 150 euros. So the euros left are $e= \frac{250}{1.3687}-150$. In a more straightforward way, we know he spent 150 euros, so the euros remaining are $e = \frac{250}{1.3687}-150=\frac{250 - 150\times1.3687}{1.3687}$. First, calculate $150\times1.3687 = 205.305$. Then $250-205.305 = 44.695$ euros left.

Step2: Convert remaining euros to US - dollars

To convert the remaining euros back to US - dollars, use the exchange rate. If 1 euro = 1.3687 US - dollars, then the amount of US - dollars $d$ he gets back is $d=44.695\times1.3687$. $d = 44.695\times1.3687=44.695\times(1 + 0.3+0.06 + 0.008+0.0007)=44.695\times1+44.695\times0.3+44.695\times0.06+44.695\times0.008+44.695\times0.0007$ $=44.695+13.4085 + 2.6817+0.35756+0.0312865\approx140.41$ US - dollars.