Write a system to model this situation

Question

 You have $22 in your bank account and deposit $11.50 each week. At the same time your cousin has $218 but is withdrawing $13 each week. When will the accounts have the same balance?

Answer 1

The key to any word problem is to identify the clues written within the problem. In other words, identify known and unknown quantities. What is unknown is the number of weeks until the accounts have the same balance. We can call that unknown item x. We know that if someone deposits money, they are adding funds to the account. On the other hand, if someone is withdrawing money, they are subtracting funds from the account. The beginning balances in each account are $22 and $218, respectively.

 

For the first account, we have the following:

 

22 + 11.50x

 

This is the initial balance plus the amount added each week.

 

For the second account, we have:

 

218 - 13x

 

When will the two accounts have the same balance? When 22 + 11.50x = 218 - 13x.

 

Can you solve this equation for x, Hunter?