please help with the following problem I have been stuck on this for 3 days now and cant grasp the concetp of what to do.

bayside insurance offers two health plans. under plan a giselle would have to pay the first $120 of her medical bills, plus 40% of the rest. under plan b giselle would pay $230, but only 35% of the rest. For what amount of medical bill will plan b save giselle money? assume she has over $230 in bills.

1st Step

Have each each scenario equal each other
120 + .40x=230+.35x
x-2200
For all amounts over 2200 plan be will save her money

To solve this problem, we need to compare the total cost for Giselle under the two health plans. We know that under plan A, Giselle would have to pay $120 plus 40% of the remainder of her medical bills. Under plan B, she would pay a fixed amount of $230 plus 35% of the remainder of her medical bills.

Let's assume Giselle's medical bill amount is x dollars (where x > $230). We can set up the equation to compare the costs of the two plans:

Cost under Plan A = $120 + 0.4(x - $120)
Cost under Plan B = $230 + 0.35(x - $230)

We want to find the amount of medical bill (x) when Plan B saves Giselle money, meaning the cost under Plan B is less than the cost under Plan A.

To solve for x, we can set the two costs equal to each other and then solve for x:

$120 + 0.4(x - $120) = $230 + 0.35(x - $230)

Simplifying the equation:
120 + 0.4x - 48 = 230 + 0.35x - 80
0.4x - 0.35x = 230 - 120 + 80 - 48
0.05x = 142

Dividing both sides by 0.05:
x = 142 / 0.05
x = 2840

Therefore, if Giselle's medical bill amount is more than $2840, Plan B will save her money compared to Plan A.