bayside insurance offers 2 plans: plan A: pay the 1st $60 + 0.30 of the rest of the bills; plan b = pay 1st $140 + 0.25 of the rest of thebills. For what amount of medical bills will plan B save money? Assume there are over $140 in bills
you want B < A, or A > B
For x dollars in bills,
A = 60 + .3(x-60)
B = 140 + .25(x-140)
60 + .30x - 18 > 140 + .25x - 35
.05x > 63
x > 1260
So, for 1260 in bills,
plan A you pay 60 + .3*1200 = 420
plan B you pay 140 + .25*1120 = 420
above that, each dollar of B costs less than for A.
To determine the amount of medical bills at which Plan B will save money, we need to set up an equation and solve for this threshold value.
Let's represent the unknown amount of medical bills as 'x'.
For Plan A, the cost will be calculated as follows:
Cost of Plan A = $60 + 0.30 * (x - $60)
For Plan B, the cost will be calculated as follows:
Cost of Plan B = $140 + 0.25 * (x - $140)
The point at which the two plans have the same cost can be found by setting the equations equal to each other:
$60 + 0.30 * (x - $60) = $140 + 0.25 * (x - $140)
Now, let's solve this equation step by step:
$60 + 0.30x - $18 = $140 + 0.25x - $35
Combining like terms:
$42 + 0.30x = $105 + 0.25x
Simplifying further:
0.30x - 0.25x = $105 - $42
0.05x = $63
Dividing both sides by 0.05:
x = $63 / 0.05
x = $1260
Therefore, for medical bills over $1260, Plan B will start saving money compared to Plan A.