Answered

Which expression can be used to convert 80 US dollars (USD) to Australian dollars (AUD)?



$\begin{array}{l}

1\text{ USD} = 1.0343\text{ AUD} \\

1\text{ AUD} = 0.9668\text{ USD}

\end{array}$


A$80\text{ USD} \times \frac{0.9668\text{ USD}}{1\text{ AUD}}$
B$80\text{ USD} \times \frac{1.0343\text{ USD}}{1\text{ AUD}}$
C$80\text{ USD} \times \frac{0.9668\text{ AUD}}{1\text{ USD}}$
D$80\text{ USD} \times \frac{1.0343\text{ AUD}}{1\text{ USD}}$

Verified Answer :

  • Start with the given amount in USD.
  • Choose the conversion rate that relates 1 USD to AUD, which is 1 USD = 1.0343 AUD.
  • Set up the multiplication such that the units cancel out, specifically using the fraction \(\frac{1.0343 \text{ AUD}}{1 \text{ USD}}\).
  • The final expression is \(\boxed{80 \text{ USD} \times \frac{1.0343 \text{ AUD}}{1 \text{ USD}}}\).

Explanation

  1. Problem Analysis

To convert an amount from one currency to another, we must use a conversion factor that allows for the cancellation of the original currency unit and the introduction of the target currency unit. In this problem, we are starting with 80 US dollars (USD) and want to find the equivalent amount in Australian dollars (AUD).

We are given two conversion rates:

  1. \(1 \text{ USD} = 1.0343 \text{ AUD}\)
  2. \(1 \text{ AUD} = 0.9668 \text{ USD}\)

We need to choose an expression of the form \(80 \text{ USD} \times \text{conversion factor}\) such that the units cancel out correctly. The desired units for our final answer are AUD, so the "USD" unit must be in the denominator of the conversion factor to cancel with the "USD" in the starting value.

  1. Selecting the Correct Expression

To convert 80 USD to AUD, we want the "USD" to cancel out, leaving us with "AUD". We can write the expression as:
\[ 80 \text{ USD} \times \frac{\text{? AUD}}{\text{? USD}} \]
Using the given rate \(1 \text{ USD} = 1.0343 \text{ AUD}\), we can construct the fraction:
\[ \frac{1.0343 \text{ AUD}}{1 \text{ USD}} \]
When we multiply these, the "USD" units cancel out:
\[ 80 \text{ USD} \times \frac{1.0343 \text{ AUD}}{1 \text{ USD}} = 80 \times 1.0343 \text{ AUD} = 82.744 \text{ AUD} \]
Comparing this to the given choices, the correct expression is \(80 \text{ USD} \times \frac{1.0343 \text{ AUD}}{1 \text{ USD}}\).

Examples

Unit conversion is essential in daily life, such as when traveling to a foreign country. If you have a budget of \(\$100\) USD and need to know how many Euros (\(\text{EUR}\)) or Japanese Yen (\(\text{JPY}\)) you will have for your trip, you use conversion rates. By multiplying your starting amount by the appropriate exchange rate (e.g., \(\text{USD} \times \frac{\text{Target Currency}}{\text{USD}}\)), you ensure your units align correctly, allowing you to manage your finances accurately while traveling.

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