SOLUTION: Bayside Insurance offers two health plans. Under plan A, Gisselle would have to pay the first $90.00 of her medical bills, plus 40% of the rest. Under plan B, Giselle would pay th

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Bayside Insurance offers two health plans. Under plan A, Gisselle would have to pay the first $90.00 of her medical bills, plus 40% of the rest. Under plan B, Giselle would pay th      Log On

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Question 449203: Bayside Insurance offers two health plans. Under plan A, Gisselle would have to pay the first $90.00 of her medical bills, plus 40% of the rest. Under plan B, Giselle would pay the first $130, but only 30% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $130 in bills. How much would Giselle save with plan B is she more than x in bills?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount she has to pay under plan A
Let b = amount she has to pay under plan B
Let x = total amount of her medical bills
given:
plan A:
+a+=+.4%2A%28x+-+90%29+%2B+90+
+a+=+.4x+%2B+54+
plan B:
+b+=+.3%2A%28x+-+130%29+%2B+130+
+b+=+.3x+%2B+91+
First I need to find the amount of bills for which +b+%3C+a+
+.3%2A%28x-130%29+%2B+130+%3C+.4%2A%28x-90%29+%2B+90+
+.3x+-+39+%2B+130+%3C+.4x+-+36+%2B+90+
+91+%3C+.1x+%2B+54+
+.1x+%3E+37+
+x+%3E+370+
If the bills are over $370, plan B costs less than plan A
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The 2nd part want you to find +b+-+a+ and solve for x
Savings = +.3%2A%28x+-+130%29+%2B+130+-%28+.4%2A%28x+-+90%29+%2B+90%29+
Savings = +.3x+-+39+%2B+130+-+.4x+%2B+36++-+90+
Savings = +37+-+.1x+
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Here's a graph of the 2 plans:
+graph%28+500%2C+500%2C+-50%2C+500%2C+-50%2C+500%2C+.4x+%2B+54%2C+.3x+%2B+91%29+