Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $60 of her medical bills, plus 30% of the rest. Plan B would pay the first $140, but only 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $140 in bills.
A= $60 +30x
B= $140 + 20x
then I get confused
To determine the amount of medical bills for which Plan B will save Giselle money compared to Plan A, we need to set up an equation and solve for x (the amount of medical bills).
Let's start by setting up the equation using the given information:
Plan A: Giselle pays the first $60 and 30% of the rest, which can be expressed as: A = $60 + 0.3x
Plan B: Giselle pays the first $140 and 20% of the rest, which can be expressed as: B = $140 + 0.2x
We want to find the amount of medical bills for which Plan B saves Giselle money. This means that the cost under Plan A (A) should be greater than the cost under Plan B (B).
So, we can set up the inequality:
A > B
$60 + 0.3x > $140 + 0.2x
To solve this inequality, we need to isolate the x variable. Start by subtracting 0.2x from both sides of the inequality:
$60 + 0.3x - 0.2x > $140
Combine like terms on the left side:
$60 + 0.1x > $140
Next, subtract $60 from both sides of the inequality:
0.1x > $140 - $60
Combine like terms on the right side:
0.1x > $80
To isolate x, divide both sides of the inequality by 0.1:
x > $80 / 0.1
This simplifies to:
x > $800
Therefore, Plan B will save Giselle money for medical bills greater than $800. Any amount below that, Plan A will be cheaper.