Bay Side Insurance Offers Two Health Plans. Under Plan A Gina Would Have To Pay The First \$180 Of Her Medical Bills, Plus 40% Of The Rest. Under Plan B, She Would Have To Pay The First \$230, But Only 25% Of The Rest. How Much Would Plan B Save Her?

You have not specified what Gina's medical bills are.

The two plans are equivalent when the bills are
180 + .40(b - 180) = 230 + .25(b - 230)    (equate the cost of the plans)
180 + .40b - 72 = 230 + .25b - 57.50    (use the distributive property)
108 + .40b = 172.50 + .25b    (collect the constant terms)
.15b + 108 = 172.50    (subtract .25b)
.15b = 64.50    (subtract 108)
b = 430    (divide by .15)

For bills greater than \$430, Plan B saves money.

The savings is the difference in cost between the two plans. We assume that Plan B is lower cost for Gina.
savings = 180 + .40(b - 180) - (230 + .25(b - 230))
= 180 + .40b - 72 - (230 + .25b - 57.50)
savings = .15b - 64.50

Example
Gina's bills are \$1000.
Her savings under Plan B are .15(1000) - 64.50 = 150 - 64.50 = 85.50.
Under Plan A, she pays 180 + .40(1000-180) = 508.00
Under Plan B, she pays 230 + .25(1000-230) = 422.50
thanked the writer. 