Question

Select ALL the correct answers.
Brandon goes to an ATM near his house and withdraws x dollars from his checking account. Since the ATM is not at the same bank where his checking account is, the bank charges a $2 fee for each transaction, which is withdrawn from his account in addition to the x dollars.

Brandon makes this same withdrawal at this same bank once a week for seven weeks. Which of the following expressions could represent the total amount withdrawn from Brandon's checking account during this time period from these ATM transactions?

(7)(x) + (7)(2)
7x + 2
7(x + 2)
7x + 9
7x + 14
(7)(x) + (7)(2x)
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Answer 1

To find the total amount withdrawn from Brandon's checking account over the course of 7 weeks, we need to consider both the amount he withdraws (x dollars) and the fee incurred for each transaction ($2).

For each transaction, Brandon withdraws x dollars and is charged an additional $2 fee. Therefore, the total amount withdrawn for one transaction is:

\[ x + 2 \]

If he makes this transaction 7 times a week for 7 weeks, the total amount withdrawn can be represented by multiplying the total for one transaction by 7:

\[ 7(x + 2) \]

Now let's evaluate the given options:

1. \( (7)(x) + (7)(2) \) - This is correct. This expression simplifies to \( 7x + 14 \).

2. \( 7x + 2 \) - This is incorrect, as it does not account for the 7 transactions.

3. \( 7(x + 2) \) - This is correct. This represents the total amount withdrawn for all transactions.

4. \( 7x + 9 \) - This is incorrect, as it inaccurately calculates the total fee.

5. \( 7x + 14 \) - This is correct, as it comes from the simplification of \( (7)(x) + (7)(2) \).

6. \( (7)(x) + (7)(2x) \) - This is incorrect. This expression miscalculates the fee as \( 2x \) instead of \( 2 \).

The correct answers are:

- \( (7)(x) + (7)(2) \)
- \( 7(x + 2) \)
- \( 7x + 14 \)