Account Balance: Linear Equation in 1 Variable

Question

Emily deposits $1200 in a savings account and withdraws $75 each month for expenses. The account balance B (in dollars) after n months can be represented by the equation B(n) = 1200 - 75n. After how many months will Emily's account balance be $525?

1. 8 months
2. 9 months
3. 10 months
4. 16 months

The account balance is given by the function B(n) = 1200 - 75n, where B is the balance in dollars and n is time in months.

1. What is to be found?:

   We need to determine after how many months the account balance will reach $525.

2. Substitute:

   We know that B(n) = 1200 - 75n represents the balance after n months.
   When balance equals $525, we can write: B(n) = 525

3. Substitute and solve:
   • B(n) = 1200 - 75n = 525
   • 1200 - 525 = 75n
   • 675 = 75n
   • Divide both sides by 75: 9 = n
4. Verify the answer: When n = 9 months, the balance should be $525.

   B(9) = 1200 - 75(9) = 1200 - 675 = 525 ✓

5. Select the correct option: Emily's account balance will be $525 after 9 months. The answer is B).