Let's determine which expression correctly converts 22 Australian dollars (AUD) to US dollars (USD) given the exchange rate of 1.2 AUD per 1 USD.
Given the information:
- 1.2 AUD = 1 USD
To convert from AUD to USD, we need to use the reciprocal of the exchange rate:
1 USD is equivalent to 1/1.2 AUD.
Thus, the expression should invert the ratio to move from AUD to USD.
Now, looking at the options:
1. [tex]\(\$ 22 \text{ AUD} \times \frac{1.2 \text{ USD}}{1 \text{ AUD}}\)[/tex]
This option uses the exchange rate directly but it's set up to convert from USD to AUD, not from AUD to USD.
2. [tex]\(\$ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}}\)[/tex]
This option correctly inverts the rate to convert AUD to USD.
3. [tex]\(\$ 1.20 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}}\)[/tex]
This option incorrectly uses [tex]\(1.20 \text{ AUD}\)[/tex] instead of [tex]\(22 \text{ AUD}\)[/tex] and should not be considered for conversion of 22 AUD.
4. [tex]\(\$ 1.20 \text{ AUD} \times \frac{1.2 \text{ USD}}{1 \text{ AUD}}\)[/tex]
This option also incorrectly starts with 1.20 AUD and uses the ratio incorrectly for converting AUD to USD.
The correct expression to use for converting 22 AUD to USD is:
[tex]\[
\$ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}}
\][/tex]
Applying this expression:
[tex]\[
\$ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} = \$ 18.333\ldots \text{ USD}
\][/tex]
Therefore, the appropriate expression to convert 22 AUD to USD is: [tex]\( \$22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} \)[/tex].
