Let’s walk through the problem step-by-step:
1. Calculate the total cost of Adam's current transactions:
Start by adding up his spending for various items:
- Car payment: \[tex]$260.16
- Groceries: \$[/tex]97.98
- Parking ticket: \[tex]$75.00
- DVD box set: \$[/tex]115.35
- Antique lamp: \[tex]$68.53
- Suit: \$[/tex]331.84
Total current transactions cost:
[tex]\[
260.16 + 97.98 + 75.00 + 115.35 + 68.53 + 331.84 = 948.86 \text{ dollars}
\][/tex]
2. Determine the current balance of Adam's account:
According to the problem, Adam's account balance should be the negative of his total current transactions cost.
So, Adam’s current balance:
[tex]\[
-948.86 \text{ dollars}
\][/tex]
3. Consider the cost of the new paint job:
The new paint job costs:
[tex]\[
264.83 \text{ dollars}
\][/tex]
4. Determine if Adam can afford the new paint job based on his current balance:
We need to compare Adam's current balance with the paint job cost:
- Current balance: [tex]\(-948.86\)[/tex] dollars.
- Paint job cost: [tex]\(264.83\)[/tex] dollars.
First Evaluation:
Check if Adam’s balance is positive or zero:
- Adam's current balance is [tex]\(-948.86\)[/tex], which means he is already in debt. Hence, we proceed to the next step.
Second Evaluation:
Check if Adam’s current balance plus the paint job cost would leave his account at zero:
- [tex]\(-948.86\)[/tex] plus [tex]\(264.83\)[/tex] equals [tex]\(-684.03\)[/tex], which is still negative.
Final Evaluation:
Check if the negative balance would become more negative by factoring in the paint job cost:
- [tex]\(-948.86\)[/tex] compared to [tex]\(-264.83\)[/tex].
Conclusion: Given the extremely negative balance and deductions, Adam is already overdrawn in his account and cannot afford any new purchases, including the new paint job.
Therefore, the best answer based on this logic:
d. No, he is overdrawn already.
