To determine the correct equation to solve for the number of monthly ATM transactions \( x \), equivalent to a \( \$ 19.50 \) monthly service fee, start by interpreting the question:
- A bank charges \( \$ 1.50 \) for each ATM transaction.
- The goal is to find out how many transactions \( x \) result in a total charge of \( \$ 19.50 \).
Let's outline the steps:
1. Each transaction costs \( \$ 1.50 \).
2. The total fee from the transactions is calculated by multiplying the cost per transaction by the number of transactions: \( 1.50 \times x \).
3. This total fee should equal \( \$ 19.50 \).
So, the equation representing the situation is:
[tex]\[ 1.50 \times x = 19.50 \][/tex]
Now, let's review the provided options to find the equation that matches this scenario:
A. \( 1.50 + x = 19.50 \) – This suggests the sum of \( 1.50 \) and the number of transactions \( x \) equals \( 19.50 \). This does not correctly represent the relationship given.
B. \( 19.50 \times x = 1.50 \) – This suggests multiplying \( 19.50 \) by the number of transactions \( x \) equals \( 1.50 \), which is not correct for our situation.
C. \( 1.50 \times x = 19.50 \) – This suggests multiplying \( 1.50 \) by the number of transactions \( x \) equals \( 19.50 \), which correctly describes the fee structure.
D. \( 19.50 + x = 1.50 \) – This suggests the sum of \( 19.50 \) and the number of transactions \( x \) equals \( 1.50 \), which is also incorrect.
Therefore, the correct equation among the options provided is:
[tex]\[ \boxed{1.50 x = 19.50} \][/tex]
To solve for the number of transactions \( x \):
[tex]\[ 1.50 x = 19.50 \][/tex]
[tex]\[ x = \frac{19.50}{1.50} \][/tex]
[tex]\[ x = 13 \][/tex]
Thus, the number of monthly ATM transactions that result in a [tex]\( \$ 19.50 \)[/tex] monthly service fee is [tex]\( 13 \)[/tex].
