(This one is one that I already have notes for. However, I can not get the answer for the life of me)
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)
i need help with my homework
To solve the problem, you're on the right track with setting up the equations for the costs of Plan A and Plan B. However, let's break down the calculation step by step to find the amount of medical bills for which Plan B would save Giselle money.
First, let's write the equation for Plan A:
Cost of Plan A = $60 + 25% of (total medical bills - $60)
Next, let's write the equation for Plan B:
Cost of Plan B = $170 + 20% of (total medical bills - $170)
We need to find the amount of medical bills for which the cost of Plan B is less than the cost of Plan A. To determine that, we need to solve the inequality:
Cost of Plan B < Cost of Plan A
Substituting the equations we derived earlier:
$170 + 0.20(total medical bills - $170) < $60 + 0.25(total medical bills - $60)
Now, let's simplify and solve the inequality step by step:
$170 + 0.20total medical bills - 0.20($170) < $60 + 0.25total medical bills - 0.25($60)
$170 + 0.20total medical bills - $34 < $60 + 0.25total medical bills - $15
$136 + 0.20total medical bills < $45 + 0.25total medical bills
Now, let's isolate the total medical bills term on one side:
0.20total medical bills - 0.25total medical bills < $45 - $136
-0.05total medical bills < -$91
To solve for total medical bills, divide both sides of the inequality by -0.05, remembering to reverse the inequality sign since you're dividing by a negative:
total medical bills > -$91 / -0.05
The negative signs cancel out, resulting in:
total medical bills > $1,820
Therefore, Giselle would save with Plan B if her medical bills were more than $1,820.
Note: It is important to understand that negative medical bills do not make sense in this context, so we can ignore that possibility and focus on positive values only.