To determine how many US dollars Mitchell has remaining after his transactions, we need to go through the following steps in detail:
1. Exchange USD to CAD:
- Mitchell starts with 150 US dollars.
- The exchange rate from USD to CAD is 0.97071.
- To find how many Canadian dollars Mitchell receives, we multiply the amount in USD by the exchange rate:
[tex]\[
\text{CAD received} = 150 \, \text{USD} \times 0.97071 \, \frac{\text{CAD}}{\text{USD}} = 145.6065 \, \text{CAD}
\][/tex]
2. Spend CAD:
- Mitchell spends 20 Canadian dollars.
- To find the amount of CAD remaining, we subtract the spent amount from the total CAD received:
[tex]\[
\text{CAD remaining} = 145.6065 \, \text{CAD} - 20 \, \text{CAD} = 125.6065 \, \text{CAD}
\][/tex]
3. Exchange CAD back to USD:
- The exchange rate from CAD to USD is given as the reciprocal of 0.97071, which is approximately 1.03069.
- To find how many US dollars Mitchell receives for the remaining Canadian dollars, we multiply the remaining CAD by the CAD to USD exchange rate:
[tex]\[
\text{USD remaining} = 125.6065 \, \text{CAD} \times 1.03069 \, \frac{\text{USD}}{\text{CAD}} = 129.3965 \, \text{USD}
\][/tex]
So, after performing all these steps, Mitchell has approximately 129.40 US dollars remaining.
Hence, the closest correct answer is:
[tex]\[ 129.46 \][/tex]
