Following is a list of bank transactions Tiana made this month. The variable, b,represents her initial balance.

Question

Deposit $275.
Withdraw $1/8b.
Withdraw $1/4b.
Deposit $320.
Which expression represents the change in her account balance this month?
Responses
595+(−3/8b)

−595+3/8b

−595+(−3/8b)

595 + 3/8b

Answer 1

To find the expression that represents the change in Tiana's account balance, we need to consider each transaction step by step:

1. Start with the initial balance, which is \( b \).

2. Deposit $275:

   • New balance = \( b + 275 \)

3. Withdraw \( \frac{1}{8}b \):

   • New balance = \( b + 275 - \frac{1}{8}b \)

4. Withdraw \( \frac{1}{4}b \):

   • \( \frac{1}{4}b \) can be rewritten as \( \frac{2}{8}b \) for easy addition.
   • New balance = \( b + 275 - \frac{1}{8}b - \frac{2}{8}b \)
   • New balance = \( b + 275 - \frac{3}{8}b \)

5. Deposit $320:

   • New balance = \( b + 275 - \frac{3}{8}b + 320 \)
   • Combine the constant terms: \( 275 + 320 = 595 \)
   • New balance = \( b - \frac{3}{8}b + 595 \)
   • \( b - \frac{3}{8}b = \frac{5}{8}b \) (because \( b = \frac{8}{8}b \))

Thus, the new balance can be expressed as: \[ \frac{5}{8}b + 595 \]

Now, the change in her account balance is given by the expression: \[ ( \text{New balance} - \text{Initial balance} ) = \left(\frac{5}{8}b + 595 - b \right) \]

Replacing \( b \) with \( \frac{8}{8}b \): \[ \frac{5}{8}b + 595 - \frac{8}{8}b = 595 - \frac{3}{8}b \]

This is the change in her account balance.

Since the change is \( 595 - \frac{3}{8}b \), we can rearrange this to match the options given: \[ -595 + \frac{3}{8}b \]

So, the answer that matches the calculation is: −595 + \( \frac{3}{8}b \).