Question

Ellis opened a checking and a savings account on the same day. His checking account had an initial balance of $1,113.50, and his savings account had an initial balance of $200.25. Each week, he withdrew $50 from his checking account and deposited $20.25 into his savings account. If he made no other withdrawals or deposits, and the balance of the two accounts are currently equal, how many weeks ago did Ellis open the accounts?

Answer 1

For the checking account:

Let set x for each week when Ellis withdrew.

The initial balance is $1,113.50

and he withdrew $50 from this account.

Then, we can write the next equation:

C=1,113.50-50x

For the saving account:

Let set x for each week when Ellis deposited.

The initial balance is $200.25

and he deposited $20.25 each week.

Then, we can write the next equation:

S=200.25+20.25x

Currently, both accounts are equal. Therefore, we can equal both equations and find the x value to know where both accounts were opened.

Then:

C = S

1,113.50-50x = 200.25+20.25x

Solve for x:

1,113.50-200.25=25x+50x

913.25= 75x

x = 12.17

12.17=x