To solve the problem, let's carefully analyze the relationship between the number of ATM transactions and the total monthly service fee.
1. The bank charges \[tex]$0.75 for each ATM transaction.
2. The total monthly service fee is \$[/tex]12.75.
3. We need to find the number of transactions, [tex]\( x \)[/tex], that result in a monthly service fee of \[tex]$12.75.
Given these points, the equation we need must relate the number of transactions \( x \) and the total service fee, which is calculated by multiplying the cost per transaction by the number of transactions.
- The cost per transaction is \$[/tex]0.75.
- The total monthly service fee is [tex]\( 0.75 \times x = 12.75 \)[/tex].
Therefore, the correct equation that represents this situation is:
[tex]\[ 0.75x = 12.75 \][/tex]
Thus, the correct answer is:
C. [tex]\[ 0.75x = 12.75 \][/tex]
Next, to find the number of transactions, we solve for [tex]\( x \)[/tex] in the equation [tex]\( 0.75x = 12.75 \)[/tex]:
[tex]\[ x = \frac{12.75}{0.75} \][/tex]
[tex]\[ x = 17 \][/tex]
Therefore, the number of monthly ATM transactions that results in a \$12.75 service fee is 17. This confirms that option C is indeed the correct equation to use.
