SOLUTION: Bayside Insurance offers two healths plan A, Giselle would have to pay the first $70 of her medical bills, plus 35% of the rest. Under plan B, Giselle would pa the first $240, but

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Bayside Insurance offers two healths plan A, Giselle would have to pay the first $70 of her medical bills, plus 35% of the rest. Under plan B, Giselle would pa the first $240, but       Log On

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Question 202719: Bayside Insurance offers two healths plan A, Giselle would have to pay the first $70 of her medical bills, plus 35% of the rest. Under plan B, Giselle would pa the first $240, but only 30% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $240 in bills.
Giselle would save with plan B if she had more than $? in bills.
(Round to the nearest whole number)
Suppose Giselle has $5000 medical bills.
Plan A would cost $ 70 + 0.35% ($5000-$70)=($4930.00)
Plan B would cost $ 240 + 0.30 ($5000-$240)=($1668.00)
240+0.30(x-240)<70+0.35(x-70)
240+0.30x-72.00<70+0.35x-24.50
168.00+0.30x<45.50+0.35x
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168.00+0.30x-0.30x<45.50+0.35x-0.30x
168.00<45.70+0.05x
122.30<0.05x
2446< x
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Can anyone tell me if I got this one right?
Thank you so much!!!!


Found 2 solutions by rfer, jim_thompson5910:
Answer by rfer(10432) About Me  (Show Source):
You can put this solution on YOUR website!
Plan A) $70 + 35%
(5000-70)*.35)+70=$1795.50
Plan B) $240 + 30%
(5000-240)*.30+240=$1668.00
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Procedure looks good on the last pat, but you made a subtraction error.
should be .05x is greater than 122.50
x is greater than 2450

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
For the first part, you're on the right track. However, in the third to last step, you made a very silly typo which gave you the wrong answer. The term "45.70" should be "45.50" which would give you the answer of x%3E2450. So if her bills are more than $2,450, then she'll save with plan B

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For the second part, simply plug in 5000 in for x into both expressions to get:

Plan A: 70%2B0.35%285000-70%29=70%2B0.35%284930%29=70%2B1725.5=1795.5

Plan B: 240%2B0.30%285000-240%29=240%2B0.30%284760%29=240%2B1428=1668


So with a bill of $5,000, she pays $1,795.50 under plan A or $1,668 under plan B (this supports the answer to the first part)