Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $50 of her medical bills, plus 30% of the rest. Under plan B, Giselle would pay the first $90, but only 25% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $90 in bills.
50 + .3(x-50) = 90 + .25 (x-90)
50 + .3 x - 15 = 90 + .25 x - 22.5
.05 x = 32.5
x = $650
To determine the amount of medical bills for which plan B will save Giselle money, we need to compare the costs of the two plans.
Let's start by finding the total cost under plan A. Giselle would pay the first $50 of her medical bills, and then 30% of the remaining amount.
So, the cost under plan A can be calculated as follows:
Cost_A = $50 + 0.3 * (total medical bills - $50)
Next, let's find the total cost under plan B. Giselle would pay the first $90 of her medical bills, and then 25% of the remaining amount.
Cost_B = $90 + 0.25 * (total medical bills - $90)
To determine the amount of medical bills for which plan B will save Giselle money, we need to find the point at which the cost under plan A exceeds the cost under plan B.
Setting Cost_A > Cost_B and solving for the total medical bills:
$50 + 0.3 * (total medical bills - $50) > $90 + 0.25 * (total medical bills - $90)
Simplifying the inequality:
$50 + 0.3 * total medical bills - $15 > $90 + 0.25 * total medical bills - $22.5
Combining like terms:
0.3 * total medical bills - 0.25 * total medical bills > $90 - $50 + $22.5 - $15
Simplifying further:
0.05 * total medical bills > $47.5
Dividing both sides by 0.05:
total medical bills > $47.5 / 0.05
Calculating the value:
total medical bills > $950
Therefore, if Giselle's medical bills exceed $950, plan B will save her money compared to plan A.