A bank offers two checking account plans. The monthly fee...

A bank offers two checking account plans. The monthly fee and charge per check for each plan are shown below. Under what conditions is it less expensive to use the Low Charge plan?
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Key Concepts

Cost Comparison

Comparing the expenses of different plans involves setting up expressions that represent each plan's cost and then establishing a relationship (usually in the form of an inequality) to determine which plan is more cost-effective under different circumstances.

Break-Even Analysis

Break-even analysis involves finding the point at which two cost functions are equal. This break-even point helps identify the threshold usage level beyond which one plan becomes more economical than the other, making it a fundamental concept in decision-making problems related to cost efficiency.

Linear Functions

In problems involving cost comparisons, costs are often modeled by linear functions that consist of a fixed fee plus a variable component that depends on the number of units (checks, in this case). Understanding how these linear functions are structured is essential for representing the costs associated with different plans.

Inequalities

Inequalities are used to express the conditions under which one cost function is less than another. This requires solving for the variable (such as the number of checks) that differentiates the costs, thus defining the range where one plan offers a cost advantage over the other.

Transcript

00:01 So in this problem, you're given two different offers for checking accounts.

00:03 You have your low charge and your fee safe.

00:05 So you're told that the monthly fee for both, one is $5, one is $1, and the charge per check for the first one is a penny, and the second one is $0.

00:15 So we want to figure out under what conditions is it less expensive to use the low charge plan.

00:21 Well, if it's less expensive, that means we need to figure out when is low charge less than fee saver.

00:29 Okay, so what we need to do is write an expression for both.

00:32 Well, low charge is going to charge you $5 per month plus an additional one cent per check.

00:39 But we don't know how many checks there are, so we're going to call that x.

00:44 Now, for fee saver, they're going to charge $1 per month plus an additional $0 .8 per check.

00:50 So we'll have to multiply $0 .8 per check.

00:53 So we'll have to solve this inequality.

00:56 So the first thing i'm going to do is get my constants on the same.

00:59 Side by subtracting one from each side of our inequality.

01:02 5 minus 1 is 4.

01:04 So we'll have 4 plus 0 .01x less than 0 .08x.

01:10 Okay.

01:11 So the next thing we're going to do is i'm going to subtract 0 .01x from both sides...

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