bayside insurance offers two health plans. under plan A, Giselle would have to pay the first $130 of her medical bills, plus 40 % of the rest. Unde plan B, Giselle would pay the first $140, but only 35% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $140 in bills.
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To determine the amount of medical bills at which Plan B would save Giselle money, we need to find the point where the total cost under Plan B is less than the total cost under Plan A.
Let's break down the costs under both plans:
For Plan A:
- Giselle would pay the first $130 of her medical bills.
- After that, she would pay 40% of the remaining amount.
For Plan B:
- Giselle would pay the first $140 of her medical bills.
- After that, she would pay 35% of the remaining amount.
To find the amount of medical bills where Plan B would save Giselle money, we can set up the following equation:
130 + 0.40(x - 130) > 140 + 0.35(x - 140)
Here, x represents the total amount of medical bills.
Let's solve the equation step by step:
130 + 0.40x - 52 > 140 + 0.35x - 49
Combine like terms:
0.05x - 52 > -210 + 0.35x
Subtract 0.35x from both sides to isolate the x term:
0.05x - 0.35x - 52 > -210
Simplify the equation further:
-0.30x - 52 > -210
Add 52 to both sides:
-0.30x > -210 + 52
Simplify the equation further:
-0.30x > -158
Now, to isolate the x term, divide both sides by -0.30 (or multiply by -1/0.30):
x < -158 / -0.30
Simplify the equation further:
x < 526.67
Since medical bills can't be negative, we take the positive value:
x < $526.67
Thus, for any total medical bill amount less than $526.67, plan B would save Giselle money.