SOLUTION: Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $180 of her medical bills, plus 40% of the rest. Under plan B, Giselle would pay the fi

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Question 326597: Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $180 of her medical bills, plus 40% of the rest. Under plan B, Giselle would pay the first $220, but only 30% of the rest. For what amount of medical bills will plan B save Giselle Money. Assume she has over $220 in bills.

Please help I don't understand at all....Thanks
Found 2 solutions by solver91311, alanc:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the amount of the medical bills. Then she is either going to pay or . The total amount of medical bills that makes these two expressions equal is the break-even amount. Less than the break even, the 180/40 plan is best. More than the break-even, the 220/30 plan is best.

Solve for to find the break-even amount.

John

Answer by alanc(27) (Show Source):
You can put this solution on YOUR website!
Say we denote medical bill by M. we don't know what M is.
The amount Giselle pays is P. So in plan A. P = .4*(M - 180) + 180 because Giselle has to pay $180 and 40% of M- 180 if M > 180.
or P = M if M <= 180
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In plan B P = .3*(M - 220) + 220 if M > 220 else P = M if M <= 220
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We have two equations: P1 = .4*(M-180) + 180
P2 = .3*(M-220) + 220
Given M > 220 we want to find out if P1 > P2 or not.
P1 = .4M + 108
P2 = .3M + 154
intersection: .4M + 108 = .3M + 154
.1M = 46
M = 460 P = 292
Test for M = 220
P1 = 196 and P2 = 220, P1 < P2
Test M = 480 P1 = 300 and P2 = 298, P1 > P2
So for 220 <= M <= 460 P1 < P2 Plan A is cheaper than Plan B
However if Medical Bills M > 460 then Plan B is cheaper than Plan A.