Question

Weston has $4,000 in his bank account and withdraws $30 a week. Evie has $2,800 in her

bank account and deposits $40 a week. When will Evie have more money than Weston (in weeks)?

Answer 1

By setting up linear equations that represent the account balances of both Weston and Evie and finding when Evie's balance is greater than Weston's, it is calculated that after 18 weeks, Evie will have more money than Weston.

Step-by-step explanation:

To determine when Evie will have more money than Weston, we need to create equations representing their respective bank account balances over time.

Let W be Weston's balance over time and E be Evie's balance over time. Initially, Weston has $4,000, and every week he withdraws $30. This can be represented by the equation W = 4000 - 30t, where t is the number of weeks. Evie starts with $2,800 and deposits $40 a week, which can be described by the equation E = 2800 + 40t.

To find out when Evie will have more money than Weston, we set E > W:

1. 2800 + 40t > 4000 - 30t
2. Adding 30t to both sides gives 2800 + 70t > 4000
3. Subtracting 2800 from both sides gives 70t > 1200
4. Dividing by 70 gives t > 1200 / 70
5. t > 17.14 weeks

Since t must be a whole number (you can't have a fraction of a week), we round up to the next full week, which is 18. Therefore, after 18 weeks, Evie will have more money in her bank account than Weston.