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Question 1151631: Parsons Bank offers two checking-account plans. The No Frills plan charges 25 cents per check whereas the Simple Checking plan costs $6 per month plus 5 cents per check. For what number of checks per month will the Simple Checking plan cost less?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Option A: 25 cents per check, which is the same as $0.25 per check
y = 0.25x is the equation for option A
x = number of checks
y = total cost in dollars
Option B: $6 per month plus 5 cents per check
x = number of checks
0.05*x = cost of writing x number of checks at $0.05 (aka 5 cents) per check
0.05x+6 = total cost after the $6 per month fee is added on
The equation for option B is y = 0.05x+6
Set up the inequality shown below to solve for x. We want to find when option B will cost lest.
(Option A's cost) > (Option B's cost)
0.25x > 0.05x+6
0.25x-0.05x > 6 ....................... subtract 0.05x from both sides
0.20x > 6
x > 6/0.20 ............................ divide both sides by 0.20
x > 30
If x > 30, then the expression 0.05x+6 is smaller than 0.25x
So if x > 30, then the Simple Checking plan is cheaper.
For instance, if x = 40, then
0.25x = 0.25*40 = 10 is the cost of option A
0.05x+6 = 0.05*40+6 = 2+6 = 8 is the cost of option B
we see that option B is cheaper if x = 40 checks are written.
Answer:
If you write more than 30 checks, then the Simple Checking Plan is the cheaper option.
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