An insurance company provides coverage for a certain dental procedure

Question

An insurance company provides coverage for a certain dental procedure according to the following rules: the policy pays 80% of the first 1200$ of cost, and 50% of the cost above 1200$. If a patient had to pay 490$ of the cost for this procedure himself, how much did the procedure cost?

(A) 1200$
(B) 1300$
(C) 1500$
(D) 1600$
(E) 1700$

(A) 1200$
(B) 1300$
(C) 1500$
(D) 1600$
(E) 1700$

Lampard42 · Answer

1200*20%+50%*(x-1200)=490; .5x-600=250, .5x=850;x=1700 IMO E

Archit3110 · Answer

given
80% of first 1200$
so customer has to pay 20% of 1200 ; 240$
so if paid 490$ ; left 250$ paid which is 50% of 500%
total bill must have been 1200+500; 1700$
IMO E

CareerGeek · Answer

For first 1200$. Patient pays 20% = 20/100*1200 = 240 $
For remaining = 490 - 240 = 250 $, his contribution = 50%

Let x be the cost above 1200 $
--> 50% of x = 250 
--> 50/100*x = 250
--> x = 250*2 = 500 $

So, Total cost of procedure = 1200 + 500 = 1700 $

IMO Option E

ScottTargetTestPrep · Answer

Let n = the total cost of the procedure. Since the insurance company pays 80% of the first $1200, then the patient pays 20% of the first $1200. The patient must also pay for 50% of the cost above $1200, which is (n - 1200). Thus, we have:

0.2(1200) + 0.5(n - 1200) = 490

240 + 0.5n - 600 = 490

0.5n - 360 = 490

0.5n = 850

n = 1,700

Alternate Solution:

Looking at the answer choices, we know the procedure costs at least 1,200$. On the first 1,200$, the patient paid 1200 x 0.2 = 240$ and thus, 490 - 240 = 250$ was the amount paid for the excess of 1,200$. Since the company and the patient pays the same amount after the first 1,200$, the operation costs 250 x 2 = 500$ more than 1,200$; i.e. 1200 + 500 = 1,700$.

Answer: E

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An insurance company provides coverage for a certain dental procedure

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An insurance company provides coverage for a certain dental procedure

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