To determine Adam's balance at the end of June, let's go through each transaction step by step and update the balance accordingly.
1. Starting balance on 4/1: [tex]$626.45
2. Transaction on 4/10: A purchase of \$[/tex]37.41
[tex]\[
\text{New balance} = 626.45 - 37.41 = 589.04
\][/tex]
3. Transaction on 4/12: A purchase of \[tex]$44.50
\[
\text{New balance} = 589.04 - 44.50 = 544.54
\]
4. Transaction on 5/3: A payment of \$[/tex]65.50
[tex]\[
\text{New balance} = 544.54 + 65.50 = 610.04
\][/tex]
5. Transaction on 5/16: A purchase of \[tex]$24.89
\[
\text{New balance} = 610.04 - 24.89 = 585.15
\]
6. Transaction on 5/20: A payment of \$[/tex]104.77
[tex]\[
\text{New balance} = 585.15 + 104.77 = 689.92
\][/tex]
7. Transaction on 6/6: A payment of \[tex]$23.60
\[
\text{New balance} = 689.92 + 23.60 = 713.52
\]
8. Transaction on 6/10: A purchase of \$[/tex]15.00
[tex]\[
\text{New balance} = 713.52 - 15.00 = 698.52
\][/tex]
9. Transaction on 6/14: A purchase of \[tex]$51.85
\[
\text{New balance} = 698.52 - 51.85 = 646.67
\]
After applying all the transactions, Adam's balance at the end of June is:
\[
\text{Final balance} = \$[/tex]646.67
\]
Therefore, none of the provided options correctly match the calculated final balance. It seems there might be an error or a misunderstanding in the problem statement or choices given, but based on our calculations, the correct balance should be \$646.67.
