The exchange rate between non-fixed currencies continually fluctuates. The chart below shows the exchange rate of the US dollar to the Japanese yen over the course of six days.

\begin{tabular}{|c|c|}
\hline Day & $¥$ \
\hline Monday & $1: 88.6122$ \
\hline Tuesday & $1: 90.8305$ \
\hline Wednesday & $1: 87.5507$ \
\hline Thursday & $1: 91.2323$ \
\hline Friday & $1: 92.7120$ \
\hline Saturday & $1: 89.4477$ \
\hline \hline
\end{tabular}

Mary has $311.75 to convert into yen. The currency exchange she is using charges a surcharge of 6% when converting currency. About how many more yen will Mary receive if she makes her trade on the day with the most favorable exchange rate than if she makes her trade on the day with the least favorable exchange rate?
A. ¥ 1,125
B. ¥ 1,513
C. ¥ 1, 609
D. ¥ 1,706

Question

The exchange rate between non-fixed currencies continually fluctuates. The chart below shows the exchange rate of the US dollar to the Japanese yen over the course of six days.

\begin{tabular}{|c|c|} 
\hline Day & $¥$ \
\hline Monday & $1: 88.6122$ \
\hline Tuesday & $1: 90.8305$ \
\hline Wednesday & $1: 87.5507$ \
\hline Thursday & $1: 91.2323$ \
\hline Friday & $1: 92.7120$ \
\hline Saturday & $1: 89.4477$ \
\hline \hline
\end{tabular}

Mary has $311.75 to convert into yen. The currency exchange she is using charges a surcharge of 6% when converting currency. About how many more yen will Mary receive if she makes her trade on the day with the most favorable exchange rate than if she makes her trade on the day with the least favorable exchange rate?
A. ¥ 1,125
B. ¥ 1,513
C. ¥ 1, 609
D. ¥ 1,706

Anonymous · Answer

Mary will receive approximately ¥1,524 more if she converts her dollars on the day with the best exchange rate than on the day with the worst. The closest answer choice is ¥1,513. Therefore, the correct answer is option B. 
 ;

GinnyAnswer · Answer

Calculate the USD available after the 6% surcharge: 311.75 × ( 1 − 0.06 ) = 293.045 . 
 Calculate the yen received at the most favorable rate (92.7120): 293.045 × 92.7120 = 27177.20034 . 
 Calculate the yen received at the least favorable rate (87.5507): 293.045 × 87.5507 = 25652.7071715 . 
 Find the difference and round to the nearest whole number: 27177.20034 − 25652.7071715 ≈ 1524 . The closest answer is 1 , 513 ​ . 
 
 Explanation 
 
 Identify Extreme Exchange Rates First, we need to identify the most and least favorable exchange rates. Looking at the table, the most favorable rate (highest yen per dollar) is 92.7120 yen per dollar on Friday, and the least favorable rate (lowest yen per dollar) is 87.5507 yen per dollar on Wednesday. 
 
 Calculate Available USD after Surcharge Next, we need to calculate the amount of US dollars Mary has available after the 6% surcharge. To do this, we multiply her initial amount by (1 - 0.06): 311.75 × ( 1 − 0.06 ) = 311.75 × 0.94 = 293.045 
So, Mary has $293.045 available for conversion. 
 
 Calculate Yen at Most Favorable Rate Now, we calculate how many yen Mary would receive at the most favorable exchange rate: 293.045 × 92.7120 = 27177.20034 
 
 Calculate Yen at Least Favorable Rate Next, we calculate how many yen Mary would receive at the least favorable exchange rate: 293.045 × 87.5507 = 25652.7071715 
 
 Find the Difference Finally, we find the difference between the two amounts: 27177.20034 − 25652.7071715 = 1524.4931685 
The difference is approximately 1524.49 yen. 
 
 Round and Choose Closest Answer Since we are asked for 'about how many more yen', we should round our answer to the nearest whole number. 1524.49 rounds to 1524. The closest answer choice is 1,513.

Examples 
 Currency exchange rates fluctuate daily, impacting international trade and travel. Understanding these fluctuations and associated fees helps individuals and businesses make informed decisions about when to convert currency. For example, a company importing goods from Japan would want to convert USD to JPY when the exchange rate is most favorable to minimize costs. Similarly, a tourist traveling to Japan would want to exchange currency when the dollar is strong against the yen to maximize their spending power. This problem demonstrates the importance of considering exchange rates and fees to optimize financial transactions in a globalized economy.

Answer (2)

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