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Use the following information to complete Exercises. Round all answers to two decimal places. 1 \(\mathrm{USD} \approx 1.07\) Canadian dollars \(\mathrm{CAD}\) \(\qquad\) 1 \(\mathrm{USD} \approx 89.85\) Japanese yen (JPY) 1 \(\mathrm{USD} \approx 0.69\) Euros \(\mathrm{EUR}\) \(\qquad\) 1 \(\mathrm{USD} \approx 7.34\) South African rand \(\mathrm{ZAR}\) 1 \(\mathrm{USD} \approx 1.16\) Australian dollars \(\mathrm{AUD}\) \(\qquad\) 1 \(\mathrm{USD} \approx 1.00 \mathrm{Swiss}\) franc \((\mathrm{CHF})\) Shyla will be driving through South Africa. She has found that the average price of gas in Johannesburg is about 19.24 ZAR per liter. a. What is this amount equivalent to in U.S. dollars? b. What is this rate equivalent to in U.S. dollars per gallon?

Short Answer

Expert verified
a) The price of gas in Johannesburg is equivalent to $2.62 per liter in U.S. dollars. b) This rate is equivalent to $9.92 per gallon in U.S. dollars.

Step by step solution

01

Convert Price Per Liter from ZAR to USD

Divide the price of gas in Johannesburg (19.24 ZAR) by the exchange rate between ZAR and USD (7.34). We do this calculation: \(19.24 \, \mathrm{ZAR}/\mathrm{liter} ÷ 7.34 \, \mathrm{USD}/\mathrm{ZAR} = 2.62 \, \mathrm{USD}/\mathrm{liter}\).
02

Convert Price Per Liter to Price Per Gallon

Then, convert price per liter to U.S. dollars per gallon, by multiplying the price in U.S. dollars per liter (found in step 1) by the volume conversion from liters to gallons: \(2.62 \, \mathrm{USD}/\mathrm{liter} \times 3.78541 \mathrm{gallons}/\mathrm{liter} = 9.92 \, \mathrm{USD}/\mathrm{gallon}\). 3.78541 is the number of liters in one gallon.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exchange Rates
Understanding the concept of exchange rates is essential when dealing with international currencies. Exchange rates are basically the price at which one currency can be converted into another. These rates fluctuate daily based on market forces such as demand and supply, political stability, and economic performance. Knowing how to interpret and use exchange rates is vital for businesses, travellers, and anyone involved in financial transactions across different currencies. For example, if 1 US dollar (USD) is equivalent to 1.07 Canadian dollars (CAD), this means that for every 1 USD you exchange, you'll receive 1.07 CAD in return. This conversion is fundamental to currency exchange activities.
Currency Conversion Mathematics
Currency conversion is more than just swapping one currency for another; it's about understanding the mathematics behind it. The basic formula involves dividing the amount of money you have by the exchange rate. For instance, if Shyla in Johannesburg wants to know how much 19.24 South African Rand (ZAR) is in US dollars (USD), she divides by the USD/ZAR exchange rate, 7.34. This yields approximately 2.62 USD per liter of gas.

To convert this amount into U.S. dollars per gallon, a common unit of measurement for gasoline in the U.S., Shyla would multiply by the number of liters in a gallon, 3.78541. This provides a conversion result that resonates with her U.S. experiences. This mathematical process is crucial for people to make informed decisions on expenditures in foreign currencies.
Financial Literacy
Financial literacy is about having the knowledge and skills to manage financial resources effectively. It encompasses understanding concepts such as exchange rates and currency conversion. When individuals like Shyla travel, they engage with a range of diverse monetary systems and value assessments. Being financially literate means being capable of making educated decisions about converting money and understanding the impact of exchange rate movements on purchasing power.

For instance, with the knowledge of exchange rates, someone can determine if it's a favorable time to exchange currencies. They can decide to wait if the exchange rates are expected to move in their favor or act immediately if not. Additionally, knowing how to calculate currency conversions can save one from relying solely on currency conversion services, which may add transaction fees, thereby saving money in the long run.

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