The exchange rate between non-fixed currencies continuously fluctuates. The table below shows the exchange rate of the US dollar to the euro over the course of six days.
| Day | $: € |
| -------- | ---------- |
| Monday | 1: 0.7102 |
| Tuesday | 1: 0.7053 |
| Wednesday| 1: 0.6869 |
| Thursday | 1: 0.6910 |
| Friday | 1: 0.7273 |
| Saturday | 1: 0.7544 |
If Rodney traded €228.75 for $314.52, when did he make his exchange?
a. Saturday
b. Friday
c. Thursday
d. Tuesday
Answer (2)
Rodney made his exchange of €228.75 for $314.52 on Friday, as his transaction rate of approximately 1.375 matches the exchange rate from that day. This was derived by calculating the exchange rate from his transaction and comparing it to the provided rates. The exchange rate on Friday, $1: €0.7273, correlates with his transaction rate.
;
Calculate the exchange rate of Rodney's transaction: 228.75 314.52 = 1.375 .
Find the day with an exchange rate that matches the calculated rate.
The exchange rate on Friday is 1 : 0.7273 , which is equivalent to 0.7273 1 ≈ 1.375 .
Therefore, Rodney made his exchange on Friday .
Explanation
Problem Analysis We are given the exchange rates between the US dollar and the euro for six days and need to determine on which day Rodney made his exchange of €228.75 for $314.52. To do this, we will calculate the exchange rate of Rodney's transaction and compare it to the given exchange rates.
Calculating the Exchange Rate First, we need to calculate the exchange rate for Rodney's transaction. This is done by dividing the amount in US dollars by the amount in euros: €228.75 $314.52 = 1.375 This means that for every 1 euro, Rodney received 1.375 US dollars.
Finding the Matching Day Now, we need to find the day when the exchange rate was approximately 1 : 0.7273 . This means that 1 US dollar was equivalent to 0.7273 euros. To find the equivalent exchange rate of euros to dollars, we need to calculate the reciprocal of 0.7273: 0.7273 1 ≈ 1.375
Determining the Day Comparing this calculated exchange rate to the table, we see that the exchange rate on Friday was 1 : 0.7273 . Calculating the reciprocal, we get approximately 1.375, which matches the exchange rate of Rodney's transaction.
Final Answer Therefore, Rodney made his exchange on Friday.
Examples
Exchange rates are used daily by individuals and businesses when converting one currency to another. For example, if you are traveling to Europe from the United States, you would need to exchange US dollars for euros. The exchange rate determines how many euros you will receive for each US dollar. Similarly, businesses that import or export goods need to use exchange rates to convert the prices of goods from one currency to another. Understanding exchange rates is crucial for making informed financial decisions when dealing with international transactions.
