bayside insurance offers two health plans. under plan A, giselle would have to pay the first 160 of her medical bills, plus 25% of the rest. under plan B, giselle would have to pay the first 180, but only 20% of the rest. for what amount of medical bills will plan B save giselle money? assume she has ove 180 in bills.
Assume her bill is $x >180,then
Equate the two plans and find when the benefits cross over:
160+0.25(x-160) = 180+0.2(x-180)
Solve for x.
I get x=480.
Since the incremental cost (0.2) is less for plan B, we conclude that plan A is advantageous up to $480 in claims, and plan B for $480 and up.
To determine the amount at which Plan B would save Giselle money, we need to find the point at which the cost under Plan A becomes higher than the cost under Plan B.
Let's break down the costs under each plan to find the amount of medical bills that triggers the savings.
Under Plan A:
- Giselle has to pay the first $160 of her medical bills
- For the remaining bills, she has to pay 25% (or 0.25) of the rest
So, the cost under Plan A can be represented as:
Cost under Plan A = $160 + 0.25(Remaining bills)
Under Plan B:
- Giselle has to pay the first $180 of her medical bills
- For the remaining bills, she has to pay 20% (or 0.20) of the rest
The cost under Plan B can be represented as:
Cost under Plan B = $180 + 0.20(Remaining bills)
To find the amount of medical bills where Plan B starts saving Giselle money, we need to set the costs equal to each other and solve for the Remaining bills:
$160 + 0.25(Remaining bills) = $180 + 0.20(Remaining bills)
Simplifying the equation gives:
0.25(Remaining bills) - 0.20(Remaining bills) = $180 - $160
0.05(Remaining bills) = $20
Remaining bills = $20 / 0.05
Remaining bills = $400
Therefore, if Giselle's medical bills exceed $400, Plan B will save her money compared to Plan A.