SOLUTION: Hello, I have used this website before and I found it incredibly useful therefor I would like a little help for one more question if possible: Darius saved $500 and wants to ope

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Question 1124616: Hello, I have used this website before and I found it incredibly useful therefor I would like a little help for one more question if possible:
Darius saved $500 and wants to open a chequing account. Ontario Trust charges $8 per month, plus $0.50 per cheque. Maple Leaf Savings charges $6 per month, plus 0.75 per cheque. Which bank offers the lower monthly charge?

I�m not quite sure if the equations are supposed to be 0.50x + 8y=500 and 0.75x + 8y=500, 0.50x + 8=500 and 0.75x=500, or something completely different. Take your time and thank you for your assistance.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
Well obviously Maple leaf offers the lowest monthly charge is no checks are written. If he does use checks however it all depends on how many! After 8 checks written with Maple leaf it becomes more expensive than Ontario.
Ontario trust with 8 checks = $ + $ = $
Maple leaf with 8 checks = $ + $ = $
Ontario trust with 9 checks = $ + $ = $
Maple leaf with 9 checks = $ + $ = $

Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website!
.

            Thanks for your high rating of this website !

Regarding your problem, the answer depends on the number of checks N. "Ontario Trust" charges 8 + 0.5*N dollars, where N is the number of checks. "Maple Leaf Savings" charges 6 + 0.75*N dollars. Until 8 + 0.5*N < 6 + 0.75*N, (*) "Ontario Trust" is cheaper. You can easily solve inequality (*). 8 - 6 < 0.75N - 0.5N 2 < 0.25N ====> N > = 8. So, if the number of checks is greater than 8, the "Ontario Trust" is cheaper. While the number of check is less than 8, the "Maple Leaf Savings" is cheaper. If N = 8, then both banks charge the same.