SOLUTION: Jim, I have tried to follow and plug in the equation but it is not working. I have been at this for over an hour and my brain is fried. Help!! Bayside Insurance offers two h

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Question 261964: Jim,
I have tried to follow and plug in the equation but it is not working. I have been at this for over an hour and my brain is fried. Help!!
Bayside Insurance offers two health plans. Under plan A Giselle would have to pay the first $140 of her bills and 25% of the rest. Under plan B she would have to pay the first $160 of her bills and 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $160 in bills.
Giselle would save with plan B if she had more than $_________in bills?
When it says assume she has over $160 in bills, does that mean you can use any number higher than 160?
Please help,
Thank you
Deborah
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The reason why we're assuming that she has over $160 in medical bills is if she had less than $160 in bills, then she would be clearly paying more for plan B. For instance, if she has $159 in bills, then she pays almost $15 more for plan B.


Let x = amount Giselle has to pay (ie her bill)

Under plan A, she has to pay the first $140 and then 25% of the rest. So if we assume that she has over $160 in bills, this means that x%3E160. After she pays the initial $140, then she has 25% of x-140 in bills left over. So this means that under plan A, the cost is c=140%2B0.25%28x-140%29


Similarly, under plan B, because "she would have to pay the first $160 of her bills and 20% of the rest", this means that the cost for plan B is c=160%2B0.20%28x-160%29



So to figure out when plan B will save her money, simply set the plan B expression less than the plan A expression


Plan_B%3CPlan_A


160%2B0.20%28x-160%29%3C140%2B0.25%28x-140%29 Substitute the given cost equations.


160%2B0.20x-32%3C140%2B0.25x-35 Distribute


128%2B0.20x%3C105%2B0.25x Combine like terms


0.20x-0.25x%3C105-128 Subtract 0.25x from both sides. Subtract 128 from both sides.


-0.05x%3C-23 Combine like terms


x%3E460 Divide both sides by -0.05. Remember that dividing both sides by a negative number will flip the inequality sign.


So if she has any bills over $460, then Plan B will cost less than Plan A.

If you're skeptical, try some values of 'x' that are around $460. Try x=400, x=450, x=500 (and maybe more) and you'll notice that plan B will become cheaper after you pass x=450.

Note: the plans cost the same when the bill is $460. This is cross over point when the plans switch in cost.