Bayside Insurance offers two health plans. Under plan A, Gisell would have to pa

Question

Bayside Insurance offers two health plans. Under plan A, Gisell would have to pay the first $150 of her medical bills, plus 25% of the rest. Under Plan B, Giselle would pay the first $240 but only 20% of the rest. For what amount of medical bills will plan b save Giselle money? Assume she has over $240 in bills.

Explanation / Answer

Assuming that her bill is over $240, we can let X represent the amount of her medical bills. This is an equation with simply one variable. We can then make the equation by using the information given to us. We pay the initial amount for each plan, and then subtract it from X to get the excess (in the parenthesis) multiplied by the percentage. Plan A is: $150 + (x-150)*.25 Plan B is: $240 + (x-240)*.20 We want to get the value of X (our bill) where Plan B requires paying LESS (so Plan B is less than Plan A). Plan A > Plan B 150 + (x-150)*.25 > 240 + (x-240)*.20 Expanding the equation gives: 150 + .25x - 37.5 > 240 + .20x - 48 Transposing the equation gives: .05x > 79.5 Because both are positive numbers, we are allowed to divide the equations by .05 to get x. Note that if we are dividing by a negative number, we have to switch > to < . Finally, you get: x > 1590 This means that for bills larger than 1590, Giselle will save by taking Plan B. Note: If you wish to imagine the graph, Plan A and Plan B are actually two lines on the graph, where Plan B has a higher vertical intersect initially, but has a smaller slope, which is the reason why it saves you more as the amount goes higher. :) Hope that helps.

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