Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same?

1 Answer
Mar 2, 2017

After four weeks you and your friend will have the same account balances.

Explanation:

Simultaneous equations are required to work this out.

Using the facts given in the question, two equations can be written:

Equation 1: #y=28+18.25x#

Equation 2: #y=161-15x#

For both of the above equations, #y# represents the total amount of money in the account, and #x# represents the number of weeks.

In the opening equations, if you consider that at week 0, the starting point, the equations would become #y=28#, and #y=161# respectively.

To find the answer, we need to subtract one equation from the other to remove #y#:

Equation 1 #-# Equation 2: #0=-133+33.25x#

This can be rearranged:

#33.25x=133#

#x=133/33.25=4#