Sue's bank account has a balance of [tex]$\$[/tex]899.83[tex]$ before she starts spending money. She makes the following transactions:
\begin{tabular}{|c|r|}
\hline
Transaction & \multicolumn{1}{|c|}{Cost (\$[/tex])} \\ \hline Rent & 353.76 \\ \hline Video game & 32.79 \\ \hline Bike maintenance & 60.26 \\ \hline Jacket & 55.62 \\ \hline Rug & 80.40 \\ \hline Night out & 35.77 \\ \hline \end{tabular}
Sue is considering splitting the cost of a new TV with her roommate. Her share would be [tex]$\$[/tex]305.22$. Can Sue afford this?
A. Yes, she can make the purchase and have money left over. B. Yes, but doing so will clear out her account. C. No, making that purchase will overdraw her account. D. No, she is overdrawn already.
Please select the best answer from the choices provided.
Let's solve this problem step-by-step by calculating Sue's potential expenses and determining whether she can afford to spend on the new TV:
1. Initial Balance: Sue starts with an initial balance of \[tex]$899.83.
2. Total Expenses:
Sue makes six transactions. Let's sum up the costs of these transactions:
\[
\begin{aligned}
\text{Rent} & : \$[/tex]353.76 \\ \text{Video game} & : \[tex]$32.79 \\
\text{Bike maintenance} & : \$[/tex]60.26 \\ \text{Jacket} & : \[tex]$55.62 \\
\text{Rug} & : \$[/tex]80.40 \\ \text{Night out} & : \[tex]$35.77 \\
\end{aligned}
\]
Adding all these amounts:
\[
353.76 + 32.79 + 60.26 + 55.62 + 80.40 + 35.77 = 618.60
\]
Thus, the total expenses sum up to \$[/tex]618.60.
3. Remaining Balance After Expenses: Subtract these total expenses from the initial balance to find out how much Sue has left before considering the TV purchase: [tex]\[
899.83 - 618.60 = 281.23
\][/tex] Sue has \[tex]$281.23 remaining after all her expenses.
4. Considering the TV Purchase:
Sue's share of the new TV is \$[/tex]305.22. Now we'll analyze her balance after purchasing the TV: [tex]\[
281.23 - 305.22 = -23.99
\][/tex] This results in a negative balance of [tex]\(-\$23.99\)[/tex].
5. Determining Affordability: Since purchasing the TV will result in a negative balance, making that purchase will overdraw her account. Therefore, she cannot afford the TV without going into a deficit.
Based on the calculations, the best answer is:
c. No, making that purchase will overdraw her account.
