Bayside Insurance offers two health plans. Under plan A, Giselle would have to p

Question

Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $50 of her medical bills, plus 25% of the rest. Under plan B, Giselle would pay the first $230, but only 20% of the rest.

For what amount of medical bills will plan B save Giselle money?
Assume she has over $70 in bills.

Explanation / Answer

The first step is to find the amount of medical bills that would cost her the same amount of money no matter her plan. The best way to do this is to find equations expressing her fees for A and B in terms of the total medical bill costs. For A she pays 50$ and then 25% of the rest, or 50+.25(x-50) dollars, where x is the total cost of medical bills. Similarly, for B she pays 230$ and then 20% of the rest, or 230+.2(x-230) dollars. We can now set these expressions equal to each other and solve for x: 50+.25(x-50)=230+.2(x-230) --> 50+.25x-12.5=230+.2x-46 --> .05x=146.5 --> x=2930. So when x=2930, the two plan A and B will both cost 770$. However, for any value of x past 2930 then A will increase faster than B and thus B will cost less. So when the amount of medical bills is greater than 2930$, plan B will save Giselle money.

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