College Algebra

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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 -

    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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