Question 452157
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bayside insurance offers two health plans. 
under plan a, giselle would have to pay the first $120 of her medical bills, plus 30% of the rest. 
under the plan b, giselle would pay the first $160 , but only 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.
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        In the post by @mananth,  his governing inequalities do not correspond to the problem,

        so they are  INCORRECT,  making the whole his solution incorrect.


        I came to solve the problem in a right way,  as it should be.



<pre>
Plan A:  120 + 0.3(x - 120),  where x is the whole medical bill value.

Plan B:  160 + 0.2(x - 160),  where x is the whole medical bill value.


The question is to find at what value of 'x' will be  plan B < plan A.


So, we should solve this inequality

    160 + 0.2(x-160) < 120 + 0.3*(x-120).


Simplify step by step

    160 + 0.2x - 32 < 120 + 0.3x - 36

    160 - 32 - 120 + 36 < 0.3x - 0.2x

             44         <     0.1x

              x         >      44/0.1 = 440.


So, plan B is more cheap than plan B at x > 440.    <U>ANSWER</U>
</pre>

Solved correctly.