Question

You have $22 in your bank account and deposit $1.50 each week. At the same time, your cousin has $225 but is withdrawing $13 each week. When will your accounts have the same balance?

a) 8 weeks
b) 10 weeks
c) 12 weeks
d) 14 weeks

Answer 1

After setting up and solving an equation for the weekly changes in both bank accounts, it's determined that it will take 14 weeks for the two accounts to have the same balance.

Step-by-step explanation:

To determine when the two bank accounts will have the same balance, we can set up an equation where the balance of your bank account grows by $1.50 each week and your cousin's account decreases by $13 each week. Starting with your $22 and your cousin's $225, these can be represented by the equations:

Your balance: $22 + $1.50 × (number of weeks)

Your cousin's balance: $225 - $13 × (number of weeks)

We can set these two equations equal to each other to find out after how many weeks the balances will be equal:

$22 + $1.50 × (number of weeks) = $225 - $13 × (number of weeks)

By combining like terms and solving for the number of weeks, we end up with:

$22 + $14.50 × (number of weeks) = $225

$14.50 × (number of weeks) = $225 - $22

$14.50 × (number of weeks) = $203

(number of weeks) = $203 / $14.50

(number of weeks) = 14

Therefore, the accounts will have the same balance after 14 weeks, which corresponds to option (d).