Answer :
To determine how much of the original 250 US dollars Phelan now has after converting to euros, spending some, and converting back to US dollars, we will follow these steps:
1. Convert US dollars to euros:
- Phelan starts with 250 US dollars.
- The exchange rate is 1 euro = 1.3687 US dollars.
- To find out how many euros he initially received, we divide his US dollars by the exchange rate:
[tex]\[ \text{Euros initial} = \frac{250 \text{ USD}}{1.3687 \text{ USD/euro}} \][/tex]
- This calculation gives us approximately 182.66 euros.
2. Calculate remaining euros after spending:
- Phelan spent 150 euros during his trip.
- To find out how many euros he has left, we subtract the spent amount from the initial euros:
[tex]\[ \text{Euros left} = 182.66 \text{ euros} - 150 \text{ euros} \][/tex]
- This equals 32.66 euros left.
3. Convert remaining euros back to US dollars:
- Now, Phelan wants to convert his remaining euros back to US dollars.
- Using the same exchange rate (1 euro = 1.3687 US dollars), we multiply his remaining euros by the exchange rate to find out how many US dollars he has left:
[tex]\[ \text{US dollars left} = 32.66 \text{ euros} \times 1.3687 \text{ USD/euro} \][/tex]
- This calculation results in approximately 44.70 US dollars.
Therefore, after converting his money to euros, spending 150 euros, and converting the remaining euros back to US dollars, Phelan now has 44.70 US dollars of the original 250 US dollars. The correct answer is:
[tex]\[ \boxed{44.70 \text{ US dollars}} \][/tex]
1. Convert US dollars to euros:
- Phelan starts with 250 US dollars.
- The exchange rate is 1 euro = 1.3687 US dollars.
- To find out how many euros he initially received, we divide his US dollars by the exchange rate:
[tex]\[ \text{Euros initial} = \frac{250 \text{ USD}}{1.3687 \text{ USD/euro}} \][/tex]
- This calculation gives us approximately 182.66 euros.
2. Calculate remaining euros after spending:
- Phelan spent 150 euros during his trip.
- To find out how many euros he has left, we subtract the spent amount from the initial euros:
[tex]\[ \text{Euros left} = 182.66 \text{ euros} - 150 \text{ euros} \][/tex]
- This equals 32.66 euros left.
3. Convert remaining euros back to US dollars:
- Now, Phelan wants to convert his remaining euros back to US dollars.
- Using the same exchange rate (1 euro = 1.3687 US dollars), we multiply his remaining euros by the exchange rate to find out how many US dollars he has left:
[tex]\[ \text{US dollars left} = 32.66 \text{ euros} \times 1.3687 \text{ USD/euro} \][/tex]
- This calculation results in approximately 44.70 US dollars.
Therefore, after converting his money to euros, spending 150 euros, and converting the remaining euros back to US dollars, Phelan now has 44.70 US dollars of the original 250 US dollars. The correct answer is:
[tex]\[ \boxed{44.70 \text{ US dollars}} \][/tex]
