How many checks should be written each month to make the credit union a better​ deal?

Question

A local bank charges ​$11 per month plus 2 cents per check. The credit union charges ​$5 per month plus 4 cents per check.

Answer 1

For bank: cost = 11 + 0.02n, where n = no. checks/mo.

For credit union: 5 + 0.04n per mo.

Set them equal and solve for n for breakeven point.

11 + 0.02n = 5 + 0.04n

6 = 0.02n and n = 300 checks/mo.

If you plot on Desmos Graphing Calculator you'll see the two line converge at 300. The bank has the higher fixed cost, so it's cheaper only if you exceed 300/mo. If less than 300/mo. use the credit union.