Question

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?

Answer 1

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`