Homework Help: College Algebra

Posted by LeAnn/I still need help please on Thursday, November 19, 2009 at 12:58am.

Bayside insurance offers two health plans. Under plan A, Giselle would have to pay the first $60 of her medical bills, plus 25% of the rest. Under plan B, Giselle would pay the first $170, but only 20% of the rest. For what amount of mediacl bills will plan B save Giselle money? Assume she has over $170 in bills.
Giselle would save with paln B if she had more than $___ in bills.

Here is part of my notes to get started but I'm not getting it after about half way through.....
Plan A would pay $60+25%($60-$170)=
Plan B would pay $170+20%($170-$170)=
Cost of Plan B $170+0.20(x-$170)
Cost of Plan A $60+0.25(x-$170)
$170+0.20(x-$170)<$60+0.25(x-$170)
$170+0.20x-(0.20)($170)<$60+0.25-(0.30)($170)
(These are the first steps)

College Algebra - Reiny, Thursday, November 19, 2009 at 8:48am
First of all, you made an error in Plan A,
should have been 60 + .25(x-60)

by setting $170+0.20(x-$170)<$60+0.25(x-$60)
you are asking for what values of x is Plan B < Plan A
That is good, now let's continue

170+0.20(x-170)<60+0.25(x-60) .... everything is in $, so we divide out the $

170 + .2x - 34 < 60 + .25x - 15
136 + .2x < .25x + 45
136 - 45 < .25x - .2x
91 < .05x
1820 < x or
x > 1820

So you found that for expenses greater than $1820 Plan B is less than Plan A

let's check it, say x = $2000
Plan A: 60 + .25(2000-60) = 545
PLan B: 170 + .2(2000-170) = 536

Checks out!

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