1490.12 – The Number One First Class Happy Bank

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.