Answer
Less than $200$ checks must be written a month in order for Credit Union to be a better deal.
Work Step by Step
To solve this exercise, we must first model the monthly costs of each bank: $$Bank_{cost} = 8 + 0.05c$$ $$Union_{cost} = 2 + 0.08c$$ where $c$ represents the amount of checks written in a month. The exercise asks us to identify how many checks must be written per month for the Credit Union to become a better deal (i.e., at what $c$ does $Bank_{cost} > Union_{cost}$): $$Bank_{cost} \gt Union_{cost}$$ $$8 + 0.05c \gt 2 + 0.08c$$ where, by solving for $c$: $$8 - 2 \gt0.08c - 0.05c$$ $$6 \gt0.03c$$ $$200 \gt c$$ These means that a customer must write less than 200 checks a month in order to make the Credit Union a better deal.
