A customer opens a savings account with an initial deposit of and deposits at the end of each week. Two weeks later, a second customer opens a savings account with an initial deposit of and deposits at the end of each week. If neither customer makes any other deposits or withdrawals, after how many weeks from the time the first customer opened their account will both accounts have the same balance?
Cevap: 8 weeks
Cevap
Both accounts will have the same balance after 8 weeks.
The correct answer is 8. Letting represent the number of weeks since the first customer opened their account, the balance of the first account can be modeled by the expression . Since the second customer opens their account two weeks later, the number of weeks they have been depositing money is . Therefore, the balance of the second account can be modeled by the expression . Setting the two expressions equal to find when the balances are the same gives the equation . Distributing the yields . Simplifying the right side gives . Subtracting and from both sides of the equation yields . Dividing both sides by gives .
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Formulating and solving linear equations in one variable from real-world contexts