bayside insurance offers two health plans. Under plan A, Giselle would have to pay the first $80 of her medical bills, plus 40% of the rest. Under plan B, Giselle would pay the first $100, but only 30% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $100 in bills. Giselle would save with plan B if she had more than $--- in bills. round to the nearest whole number.

Question

bayside insurance offers two health plans.  Under plan A, Giselle would have to pay the first $80 of her medical bills, plus 40% of the rest.  Under plan B, Giselle would pay the first $100, but only 30% of the rest.  For what amount of medical bills will plan B save Giselle money? Assume she has over $100 in bills.  Giselle would save with plan B if she had more than $--- in bills.  round to the nearest whole number.

amistre64 · Answer

a(x) = 80 + .4x

b(x) = 100 +.3x

amistre64 · Answer

when they equal we have an equilibrium and anything past it flips the money

amistre64 · Answer

100 +.3x = 80 + .4x   ; -.3x and -80

20 = .1x

x = 20/.1 = 200/1 = 200

amistre64 · Answer

plan b saves money for anything over 200 dollars

anonymous · Answer

Hi amistre64 i posted the answer and 200 is not correct

amistre64 · Answer

then i probably left out something ....

anonymous · Answer

would you double check for me please if its not asking too much

amistre64 · Answer

i will, but make sure you are apllying the right format to your answer in the program your using too

anonymous · Answer

This is the question at the end that needs the answer
Giselle would save with plan B if she had more than $--- in bills.  round to the nearest whole number.

amistre64 · Answer

well; when the bill costs 50 lets say; then she pays out of pocket 50 dollars..... and if we plug in a 50 here it doesnt say 50...so i prolly missed something

anonymous · Answer

so 50 is the answer

amistre64 · Answer

50 was just a test

amistre64 · Answer

the bill comes in; and its say 500

500 - 80 = whats left

.4 (500-80) = what she owes for it;

.4(530) = 212; so she pays a total of .4(B-80) + 80

amistre64 · Answer

lets test that with 400 dollar bill

.4(400-80) + 80 = Payment of 208 out of pocket

looks good

amistre64 · Answer

if the bill = 80 then; we get .4(0) + 80 = 80 out of pocket

amistre64 · Answer

.4B -32+80 = .4x +48 for plan a then right?

amistre64 · Answer

.3(x-100)+100

.3x -30+100

.3x +70 for plan b

amistre64 · Answer

now we can equate them

.4x +48 = .3x +70

.1x = 22

x = 220 .... maybe?

anonymous · Answer

hot dog amistre64 you're awesome that is correct thank you you are a life saver

amistre64 · Answer

:) youre welcome