SOLUTION: Here is the problem. You need to open a checking account and decide to shop around for a bank. Acme Bank has an account with a $10.00 monthly charge, plus a 25-cent charge per chec

Question 578471: Here is the problem. You need to open a checking account and decide to shop around for a bank. Acme Bank has an account with a $10.00 monthly charge, plus a 25-cent charge per check. Farmer's Bamk will charge you $12 per month, with a 20-cent charge per check. How many checks would you need to write each month to make Farmer's Bank the better deal?
I know there is a $2.00 difference in the monthly charge and a $.5 difference im the charge per check. I divide the $2.00 by .5 to get 4 checks but I think I am still missing something.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let n be the number of checks
The cost per month for these banks will be
Acme Bank 10 + 0.25 n
Farmers bank 12 + 0.20 n
Acme Bank > Farmers bank
10 + 0.25 n > 12 + 0.20 n
add -10 to both sides
10+0.25 n-10 >12+0.20n-10
0.25n-12>0.2n+ 2
add -0.2 n
0.05 n > 2
/ 0.05
n < 40
n should be less than 40 for Acme Bank to be a better deal

CHECK

Plan A = Plan B at 40 checks
Plan A( Acme) 10 + 0.25 * 40 = 20
Plan B ( farmers)12 + 0.20 * 40 = 20

Plan A >Plan B for 45 checks
Acme Bank 10 + 0.25 * 45 = 21.25
Farmers bank 12 + 0.20 * 45 = 21

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