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)
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!
To determine the amount of medical bills for which Plan B will save Giselle money, we need to find the threshold where the cost of Plan B becomes less than the cost of Plan A.
Let's continue solving the equation:
$170 + 0.20x - (0.20)($170) < $60 + 0.25 - (0.30)($170)
Simplifying both sides and distributing the percentages:
$170 + 0.20x - (0.20)($170) < $60 + 0.25x - (0.30)($170)
$170 + 0.20x - $34 < $60 + 0.25x - $51
Combining like terms:
$136 + 0.20x < $60 + 0.25x - $51
Moving the variables to one side and constants to the other side:
0.20x - 0.25x < $60 - $51 - $136
-0.05x < -$127
Now, divide by -0.05 to solve for x:
x > -$127 / -0.05
Remember, when we divide an inequality by a negative number, we need to flip the inequality sign:
x > $2,540
Therefore, Giselle would save with Plan B if she had more than $2,540 in medical bills.