Question

Mrs. Trout had $300 in her bank account. Mrs. Trout went to the bank 10 times during the month of November. Each time she went, she either deposited $50 or withdrew $25 from her account. At the end of the month, she has $350 in the account. Explain what she did on each of the 10 visits. Show all work and calculations to support your answer.

Answer 1

Mrs. Trout made 4 deposits of $50 and 6 withdrawals of $25 during the month of November. This was calculated using two equations representing the number of transactions and the net change in her account balance.

Step-by-step explanation:

Mrs. Trout started with $300 in her bank account and made 10 transactions during November, either depositing $50 or withdrawing $25 each time. By the end of the month, her account balance increased to $350. To calculate how many deposits and withdrawals she made, we can set up two equations based on the total number of transactions (10) and the net change in her account ($50, which is $350 - $300).

Let's let D represent the number of $50 deposits and W represent the number of $25 withdrawals. We can establish the following equations:

• D + W = 10 (since she made 10 total transactions)
• 50D - 25W = 50 (the net increase in her account)

Multiplying the first equation by 25 to align the coefficients and eliminate W gives us:

• 25D + 25W = 250
• 50D - 25W = 50

Adding these equations, we get:

• 75D = 300

Dividing both sides by 75:

• D = 4

Substituting D = 4 back into the first equation:

• 4 + W = 10
• W = 6

Therefore, Mrs. Trout made 4 deposits of $50 and 6 withdrawals of $25 during the month of November.