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Using credit is one of the most important factors in calculating a credit rating. Credit use is calculated as:
[tex]$
\begin{array}{c}
\frac{\text{Total Balance}}{\text{Total Credit Limit}} = \text{Credit Use} \\
\text{Credit Use} \cdot 100 = \%
\end{array}
$[/tex]

The lower the percent, the better the credit score. Consider these three credit cards.
\begin{tabular}{|c|c|c|}
\hline & Balance & Credit Limit \\
\hline Card A & \[tex]$800 & \$[/tex]1000 \\
\hline Card B & \[tex]$2000 & \$[/tex]5000 \\
\hline Card C & \[tex]$3000 & \$[/tex]10,000 \\
\hline Total & \[tex]$5800 & \$[/tex]16,000 \\
\hline
\end{tabular}

The overall credit use is [tex]$36.25\%$[/tex]. Card A is [tex]$80\%$[/tex]. How much would the credit use percentage be if Card A had a zero balance? Round to the nearest hundredth.

A. [tex]$34.84\%$[/tex]
B. [tex]$31.25\%$[/tex]
C. [tex]$37.42\%$[/tex]
D. [tex]$30\%$[/tex]



Answer :

GinnyAnswer
To find out how much the credit use percentage would be if Card A had a zero balance, follow these steps:

1. Identify the original balances and credit limits for each card:
- Card A: Balance = \[tex]$800, Credit Limit = \$[/tex]1000
- Card B: Balance = \[tex]$2000, Credit Limit = \$[/tex]5000
- Card C: Balance = \[tex]$3000, Credit Limit = \$[/tex]10000

2. Calculate the original total balance and total credit limit:
- Total Balance = \[tex]$800 (Card A) + \$[/tex]2000 (Card B) + \[tex]$3000 (Card C) = \$[/tex]5800
- Total Credit Limit = \[tex]$1000 (Card A) + \$[/tex]5000 (Card B) + \[tex]$10000 (Card C) = \$[/tex]16000
- The overall credit use percentage with these values is [tex]\( \frac{\$5800}{\$16000} \times 100 = 36.25 \% \)[/tex].

3. Adjust for a zero balance on Card A:
- If Card A had a zero balance, the balance of Card A would change from \[tex]$800 to \$[/tex]0.
- New Total Balance = \[tex]$0 (Card A) + \$[/tex]2000 (Card B) + \[tex]$3000 (Card C) = \$[/tex]5000
- The Total Credit Limit remains the same at \[tex]$16000. 4. Calculate the new credit use percentage: - New Credit Use = \( \frac{\$[/tex]5000}{\[tex]$16000} \) - Converting this to a percentage: \( \left( \frac{\$[/tex]5000}{\$16000} \right) \times 100 = 31.25\% \).

Thus, the credit use percentage would be [tex]\(31.25 \%\)[/tex] if Card A had a zero balance.

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