Algebra word problem help?
Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $70 of her medical bills, plus 30% of the rest. Under plan B, Giselle would pay the first $220, but only 20% of the rest. For what amount og medical bills will B save Giselle money. Assume she has over $220 in bills.
Giselle would save with plan B if she had more than $(Answer?) in bills.
Comments
x = her bill
70 + 0.3(x - 70) = 220 + 0.2(x -220]
x = 1270
If she has bill more than $1270 , plan B is better.
Plan A: out of pocket = 70 + 0.3x
Plan B: out of pocket = 220 + 0.2x
If Plan B is a better plan, 220 + 0.2x < 70 + 0.3 x
You solve the inequality and you get x >1500. So if her medical bills are greater than 1500, Plan B is better.
This is how you solve the inequality.
Subtract 70 from both sides. This gives you 150 + 0.2x < 0.3x.
Subtract 0.2x from both sides. This gives you 150 < 0.1x.
Multiply both sides by 10. This gives you 1500 < x, which is the solution.
You need to find where plan A is more than plan B, so set up an inequality to solve for X, X being the point any costs above that would cause her to spend more on Plan A vs Plan B
70 + .30X > 220 + .20X
Combine like terms
70 + .30X - 70 - .20X > 220 + .20X - 70 - .20X
.10X > 150
.10X/.1 > 150/.1
X > 1500
PROOF
70 +.3(1501) > 220 + .2(1501)
70 + 450.03 > 220 + 300.2
520.03 > 520.02
70 + 30%(A -- 70) = 220 + 20%(A -- 220) whence A = [80%220 -- 70%70] / 10% = 1270
More than $1270