1490.12 – The Number One First Class Happy Bank

The Number One First Class Happy Bank charges you 25 cents a month plus 10 cents per check. Now they are raising the service charge to 50 cents per month while reducing the per check charge to 8 cents.

Should you be happy with the change?

Solution

Let $x$ be the number of checks you plan to write. The problem asks, essentially, for the break-even point, that is, the value of $x$ at which the old charges of $25 + 10x$ equal the new charges of $50 + 8x$ .

This takes algebra! We solve:

\begin{aligned} 25 + 10x &=& 50 + 8x \\ 2x &=& 25 \\ x &=& 12.5 \end{aligned}

So, try writing 12 checks and 13 checks under both systems. You'll see that if you write 13 or more checks, you will pay less with the new charges; if you write 12 or fewer, you will pay less with the old charges.

Whether you'll be happy with the change depends on how many checks you typically write in a month.