Question 145950
"For what amount of medical bills will plan B save Giselle money?"


Let x=amount of the bill


Under plan A, the expression is 


{{{50+0.25(x-50)}}}



Under plan B, the expression is 


{{{230+0.20(x-230)}}}




So to figure out when plan B will save her money, simply set the plan B expression less than the plan A expression



{{{Plan_B<Plan_A}}}



{{{230+0.20(x-230)<50+0.25(x-50)}}}



{{{230+0.20x-46<50+0.25x-12.5}}} Distribute



{{{184+0.20x<37.5+0.25x}}} Combine like terms



{{{0.20x-0.25x<37.5-184}}} Subtract 0.25x from both sides. Subtract 184 from both sides. 



{{{-0.05x<-146.5}}} Combine like terms



{{{x>2930}}} Divide both sides by 0.45



So if she has any bills over $2,930, then Plan B will cost less than Plan A. 





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"Suppose Giselle has a certain amount in medical bills, such as $5000.  How much would she pay under each plan?"


{{{50+0.25(x-50)}}} Start with the Plan A expression



{{{50+0.25*(5000-50)}}} Plug in {{{x=5000}}} 



{{{50+0.25*4950}}} Subtract {{{50}}} from {{{5000}}} to get {{{4950}}}.  



{{{50+1237.5}}} Multiply {{{0.25}}} and {{{4950}}} to get {{{1237.5}}}.  



{{{1287.5}}} Add {{{50}}} and {{{1237.5}}} to get {{{1287.5}}}.  




So under Plan A, she will pay $1,287.50




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{{{230+0.20(x-230)}}} Start with the Plan B expression




{{{230+0.20*(5000-230)}}} Plug in {{{x=5000}}} 



{{{230+0.20*4770}}} Subtract {{{230}}} from {{{5000}}} to get {{{4770}}}.  



{{{230+0954}}} Multiply {{{0.20}}} and {{{4770}}} to get {{{954}}}.  



{{{1184}}} Add {{{230}}} and {{{954}}} to get {{{1184}}}.  




So under Plan B, she will pay $1,184.00