MathMath thank for showing me my mistake.
Bayside Insurance offers two health plans. Under Plan A, Sam would have to pay the first $200 of his medical bills, plus 35% of the rest. Under Plan B, Sam would pay the first $230, but only 20% of the rest. For what amount of medical bills will Plan B save Sam money? Assume he was over $230 in bills. Sam would save with Plan B if he had more than $_____ in bills
For what total bill X does
200 + 0.35 (X-200) = 230 + 0.20(X-230) ?
Solve for X.
200 -70 +0.35X = 230 -46 +0.20X
0.15X = 54
X = 360
To determine the amount of medical bills for which Plan B would save Sam money, we need to establish an equation and solve for the missing value.
Let's break down the two health plans' costs in terms of Sam's medical bills:
Plan A: Sam pays the first $200 plus 35% of the remaining medical bills.
Plan B: Sam pays the first $230 plus 20% of the remaining medical bills.
Let's represent the amount of medical bills with the variable "x" (since it is unknown).
For Plan A, the cost would be: $200 + 35% of (x - 200) -> $200 + 0.35(x - 200).
For Plan B, the cost would be: $230 + 20% of (x - 230) -> $230 + 0.20(x - 230).
Now, we can set up an equation to find the value of x (the amount of medical bills for which Plan B would save Sam money):
$200 + 0.35(x - 200) > $230 + 0.20(x - 230).
To solve this equation, we can simplify and solve for x:
$200 + 0.35x - 70 > $230 + 0.20x - 46.
Combine like terms:
0.35x - 20 > 0.20x - 16.
Rearrange the equation by moving similar terms to one side:
0.35x - 0.20x > -16 + 20.
0.15x > 4.
Divide both sides by 0.15 to isolate x:
x > 4 / 0.15.
Calculating this, we find:
x > 26.67.
Therefore, Sam would save with Plan B if he had more than $26.67 in medical bills.