|
Question 1118802: Mr. Jones has two health insurance policies. For the first policy he pays $120 a year which entitles him to 80% of his covered medical expenses after the insured pays the first $100.the premium for the second policy is $90 for which the company will pay 25% of his medical bill plus 20% of the amount which the first company pays. Find the amount of a medical bill which the insured may incur during a year so that he will recover exactly the medical bill plus the cost of the two premiums.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this is what i get, assuming i understand the problem correctly.
company A costs 120 per year.
it pays 80% of the medical bills after the deductible of 100 has been paid.
if x is the medical bills for the year, then it pays .8 * (x - 100).
simplify this to get that company A pays .8 * x - 80.
company B costs 90 per year.
it pays 25% of the medical bills plus 20% of what company A pays.
if x is the medical bills for the year, then it pays .25 * x + .2 * (.8 * x - 80).
simplify this to get company B pays .25 * x + .16 * x - 16.
combine like terms to get company B pays .41 * x - 16.
the total that the two companies pay is:
.8x - 80 plus .41 * x - 16.
combine like terms to get the total that the two companies pay is:
1.21 * x - 96.
that has to equal the total cost of both premiums plus what the medical bills cost for the year.
that would be 120 + 90 + x = 210 + x.
you need to solve for x in the following equation.
210 + x = 1.21 * x - 96
subtract x from both sides of this equation and add 96 to both sides of this equation to get:
306 = .21 * x.
solve for x to get x = 306 / .21 = 1457.142857.
that's what his medical bills have to be for the year so that he breaks even, which means that the cost of his medical bills plus the cost of the premiums is exactly equal to what the insurance companies pay.
let's see if that works.
the total medical bills for the year are 1457.142857.
company A pays 80% of that after the deductible of 100 has been paid.
therefore, company A pays .8 * (1457.142857 - 100) = 1085.714286.
company B pays 25% of the medical bills plus 20% of what company A pays.
that would be .25 * 1457.142857 plus .2 * 1085.714286 = 581.4285714.
the total that both companies pay is 1085.714286 plus 581.4285714 = 1667.142857.
the two premiums plus the cost of the medical bills is equal to 120 + 90 + 1457.142857 = 1667.142857.
your solution is that the total medical bills for the year must be equal to 1457.142857 for the cost of the two premiums plus the cost of the medical bills to be exactly equal to what both insurance companies pay.
|
|
|
| |
