Bayside Insurance offers two health plans. Under plan A Gisielle would pay the first $110 of her medical bills plus 30% of the rest. Under plan B, Gisielle would pay the first $250, but only 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $250 in bills. (I get to where I almost have it but it is still wrong.)
let the medical bills be x
Plan A : Cost = .3x + 110
Plan B : Cost = .2x + 250
.3x + 110 = .2x + 250
.1x = 140
x = 1400
They are equal at $1400, can you figure out which is best over $1400 ?
Hint: try both equations using 1500
To determine for what amount of medical bills Plan B will save Giselle money, we need to set up an equation and solve for the point where the cost under Plan A equals the cost under Plan B.
Let's define the amount of medical bills as "x". We can express the cost under Plan A as follows:
Cost under Plan A = $110 + 30% of the rest
= $110 + 0.3(x - $110)
= $110 + 0.3x - $33
Similarly, the cost under Plan B can be expressed as:
Cost under Plan B = $250 + 20% of the rest
= $250 + 0.2(x - $250)
= $250 + 0.2x - $50
Now, we can set up an equation to find when the cost under Plan B is less than the cost under Plan A:
$110 + 0.3x - $33 > $250 + 0.2x - $50
Simplifying this equation, we get:
0.3x - 0.2x > $250 - $50 + $33 - $110
0.1x > $123
Dividing both sides by 0.1, we find:
x > $1230
Therefore, for medical bills greater than $1230, Plan B will save Giselle money compared to Plan A.