Question 452157: bayside insurance offers two health plans. under plan a, giselle would have to pay the first $120 of her medical bills, plus 30% of the rest. under the plan b, giselle would pay the first $160 , but only 20% of the rest. for what amount of medical bills will plan b save giselle money? assume she has over $160 in bills giselle would save with plan b if she had more than $ in bills.
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Plan A 120 + 0.3 x
Plan B 160 + 0.2 x
Plan A > Plan B
300 + 0.1 x > 500 + 0.03 x
0.1 x -0.03 x > 500 -300
0.07 x > 200
/ 0.07
x> 200 / 0.07
x> 2857.14
For x> 2857 Plan A expensive
OR Plan B will save money
Answer by ikleyn(53751)  (Show Source):
You can put this solution on YOUR website! .
bayside insurance offers two health plans.
under plan a, giselle would have to pay the first $120 of her medical bills, plus 30% of the rest.
under the plan b, giselle would pay the first $160 , but only 20% of the rest.
for what amount of medical bills will plan b save giselle money?
assume she has over $160 in bills giselle would save with plan b if she had more than $ in bills.
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In the post by @mananth, his governing inequalities do not correspond to the problem,
so they are INCORRECT, making the whole his solution incorrect.
I came to solve the problem in a right way, as it should be.
Plan A: 120 + 0.3(x - 120), where x is the whole medical bill value.
Plan B: 160 + 0.2(x - 160), where x is the whole medical bill value.
The question is to find at what value of 'x' will be plan B < plan A.
So, we should solve this inequality
160 + 0.2(x-160) < 120 + 0.3*(x-120).
Simplify step by step
160 + 0.2x - 32 < 120 + 0.3x - 36
160 - 32 - 120 + 36 < 0.3x - 0.2x
44 < 0.1x
x > 44/0.1 = 440.
So, plan B is more cheap than plan B at x > 440. ANSWER
Solved correctly.
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