# 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!