Question 547408
For expenses up to $170, both plans make you pay the total balance.
Between $170 and $190, plan A is obviously cheaper, because with plan A you pay less than the total balance, while B makes you pay the whole balance.
For expenses over $190, if the total medical bills amount to x (in $), you would have to pay an amount y (in $) that varies like this:
with plan A, {{{y=170+0.4(x-170)=170+0.4x-68=0.4x+102}}}
with plan B, {{{y=190+0.2(x-190)=190+0.2x-38=0.2x+152}}}
Although your cost with plan A start lower at {{{x=190}}}, they increase more steeply with x (greater slope) and the lines intersect where
{{{0.4x+102=0.2x+152}}}
Subtracting 0.2x from both sides:
{{{0.2x+102=152}}}
Subtracting 102 from both sides:
{{{0.2x=50}}}
Multiplying both sides by 5 (or dividing both by 0.2, same thing):
{{{x=250}}}
If your medical bills are $250, you would pay $202 with either plan:
with plan A, {{{y(250)=0.4*250+102=100+102=202}}}
with plan B, {{{y(250)=0.2*250+152=50+152=202}}}
For medical expenses between $170 and $250, plan B costs more than plan A.
For more than $250, plan A costs more.