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

To find how many checks would need to be written to make the credit union a better deal than the local bank, we first need to set the two equations equal to each other. This will allow us to find how many checks need to be written for each bank to equal the other in costs.

C - Credit Union & B - Local Bank. I will use x for the variable number of checks.

C= 5 + 0.04x

B= 11 + 0.02x

Setting the two equations equal to each other:

5 + 0.04x = 11 + 0.02x

Step 1: Bring all the variables (x) to one side. Subtract the smaller side from both the left and right sides of the equal sign.

5 + 0.04x = 11 + 0.02x

-0.02x = -0.02x

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5 + 0.02x = 11

Step 2: Subtract away any constants or other numbers to isolate the variable x and its coefficients on one side of the equation sign.

5 + 0.02x = 11

-5 = -5

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0.02x = 6

Step 3: Now divide both sides by the coefficient of x.

(0.02x) / 0.02 = 6 / 0.02

x = 6/ 0.02 = 300

So for the cost of the bank to equal the cost of the credit union, we need to write 300 checks. Because the credit union has a higher cost per check (4 cents/check) than the bank (2 cents/check), we will want to write no more than 300 checks per month. We can prove this by plugging in 299 and 301 checks for our variable x.

Local Bank: f(x)= 11+0.02(x), f(299)= 11+0.02(301) = 11+5.98= $16.98

Credit Union: f(x)= 5+0.04(x), f(299)= 5+0.04(299) = 5+11.96= $16.96

At 299 checks, the cost of the credit union is less than the cost of the local bank.

Local Bank: f(x)= 11+0.02(x), f(301)= 11+0.02(301) = 11+6.02= $17.02

Credit Union: f(x)= 5+0.04(x), f(301)= 5+0.04(301) = 5+12.04= $17.04

At 301 checks, the cost of the credit union is more than the local bank.

So, for the credit union to be the better, cheaper option. The checkbook owner should write no more than 299 checks per month to save money and no more than 300 checks per month to break even.