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Re: Insurance Plan A requires the patient to pay up to the first [#permalink]
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It looks like there are some formatting issues in the question and answer options
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Re: Insurance Plan A requires the patient to pay up to the first [#permalink]
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Fixed. Thank you for pointing out
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Re: Insurance Plan A requires the patient to pay up to the first [#permalink]
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First thing I did was set up 2 equations for each insurance when the bill exceeds the minimum payment requirement
A = 1600 + 0.12(x-1600)
B = 2000 + 0.08(x)
We know that under plan A the patient pays the full amount if it's under or = 1600, same goes for B if the total is under 2000, so instantly options A and B are valid.
I ruled out C because plan B would pay the full 1840, whereas A would pay less (just by glancing at the earlier equation, the actual value A would pay is 1628.8)
Once you hit 2000 on plan B, you have to pay 2000+0.08(total) [this is where word problems get tricky], so I knew that D wasn't a valid option because plan B would pay more than 2000 and A would pay less than 2000
From there, I plugged options E, F, and G into the earlier equations to get my final answer of A,B, and G.

I'm willing to bet there's a quicker way to solve this problem, this was just how I set it up
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Re: Insurance Plan A requires the patient to pay up to the first [#permalink]
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To complete the previous answer, especially to show that 14,800 is the answer:

For any amount less than 1600 you know you will pay the same amount under both plans. Because they require you to pay your bill basically.
Then, let's look at an amount x between 1600 and 2000, 1600 < x <= 2000
Under plan A you pay 1600 + (x-1600)x0.12.
Under plan B you will always pay x
When are those things equal? Only when x=1600 (but it's not in the range we're considering).

Now let's look at an amount x > 2000
Then under plan A you pay
1600 + 0.12(x-1600)
Under plan B you pay
2000 + 0.08 x
When are those things equal?
1600 + 0.12(x-1600)=2000 + 0.08x
0.04 x = 400 + 0.12x1600
x=14,800

So we can tick any box below (less than or equal) 1600 and equal to 14,800.
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Re: Insurance Plan A requires the patient to pay up to the first [#permalink]
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Re: Insurance Plan A requires the patient to pay up to the first [#permalink]
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