求教一道manhattan上的模考题

疯愁怂狗子

Health insurance Plan A requires the insured to pay $1,000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
答案  600  1000 3800   5300   6200，  答案是第三个
实在不懂解析为什么那样算  ，
We can approach this problem in two ways. The first, and probably easier, method is to work backward from the answer choices and calculate how much Plans A and B pay out in each case. When the two calculated amounts are the same, we will have found our answer. For example, when the total cost is $600, Plan A requires the insured to pay $300, and the insurance plan pays the remaining $300. In contrast, Plan B requires the insured to pay the initial $300, and 20% of the excess of $600 – $300 = $300, which amounts to a total of $300 + (20%) × $300 = $360 out of the pocket of the insured. The plan pays for the remaining $240. We can see that the two amounts are not the same, so A is not our answer. We would then proceed to check the remaining answer choices in a similar manner.

An algebraic approach is the other possibility. First we need to determine how much Insurance Plan A pays. The question states that the insured pays either $1,000 or 50% of the total cost, whichever is lower. Let x be the total cost. If the insured pays $1,000, then the insurance plan pays x – 1000. If the insured pays 50% of the total cost, then the insurance plan also pays 50% of the cost, or 0.5x.

For Insurance Plan B, the insured pays the first $300, and the insurance plan pays 80% of everything over $300. So Insurance Plan B pays 0.8(x - 300).

Because there are two possible payment structures for Plan A, so we need to set up 2 equations. We are looking for the cost level for which both plans pay out the same amount, so we can set the two plans equal to each other. The two equations are:

0.8(x – 300) = x – 1,000 OR 0.8(x – 300) = .5x

Solving the first equation gives us x = 3,800, and solving the second equation gives us x = 800.

$800 isn't one of our options, but $3,800 is.

The correct answer is C.

疯愁怂狗子

“If the insured pays $1,000, then the insurance plan pays x – 1000.” 为什么不直接是[1000, 50%t]min?

unicorn0130

给你解释一下题意你就明白了，保险公司有co-pay, plan A 是投保人付1000 co-pay,剩下的保险公司付(x-1000)；或者投保人和公司各付费用的50%,即0.5x（whichever is lower),这两个option不能同时存在。；plan B投保人付300，保险公司付全部费用-300的80%。问费用多少时A,B plan保险公司付的钱一样多.

疯愁怂狗子

哦哦 明白了，我把投保人付的看作是保险公司要付的部分了  Thanks!!