Final answer:
Kenneth will need to save for 10 months to reach $2475 in his bank account, starting with $725 and depositing $175 monthly. By setting up a linear equation and solving for the number of months (M), we find M to be 10.
Step-by-step explanation:
Kenneth wants to determine how many months it will take to have $2475 in his bank account, starting with $725 and depositing $175 each month. To find this, we can set up a linear equation that models the total amount of money in the account, which is the initial deposit plus the consistent monthly deposits over time.
Setting up the equation
Let M be the number of months needed. The initial amount is $725, and the monthly deposit is $175. Therefore, the equation modeling the total amount is:
Total Amount = Initial Deposit + (Monthly Deposit × Number of Months)
$2475 = $725 + ($175 × M)
Solving the equation
First, subtract the initial deposit from both sides:
$2475 - $725 = $175M
$1750 = $175M
Now divide both sides by the monthly deposit amount:
$1750 / $175 = M
So, M = 10
It will take Kenneth 10 months to have $2475 in his bank account.