Question 326597
Say we denote medical bill by  M.  we don't know what M is.

The amount Giselle pays is P.   So  in plan A.  P = .4*(M - 180) + 180  because Giselle has to pay $180 and 40% of M- 180  if M > 180.
or P = M if M <= 180

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In plan B  P = .3*(M - 220) + 220  if M > 220   else P = M   if M <= 220

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We have two equations:   P1 = .4*(M-180) + 180
                         P2 = .3*(M-220) + 220

Given M > 220  we want to find out if P1 > P2 or not.

P1 = .4M + 108
P2 = .3M + 154

intersection:  .4M + 108 = .3M + 154

.1M = 46

M = 460  P = 292

Test for M = 220
P1 = 196 and P2 = 220,  P1 < P2

Test M = 480 P1 = 300  and P2 = 298, P1 > P2

So  for   220 <= M <= 460  P1 < P2  Plan A is cheaper than Plan B
However if  Medical Bills M > 460  then Plan B is cheaper than Plan A.