SOLUTION: I have been struggling with this equation and what I have come up with just does not sound right, could someone help me? Household Income. Alkena and Hsu together earn $84,326 p

Algebra ->  Finance -> SOLUTION: I have been struggling with this equation and what I have come up with just does not sound right, could someone help me? Household Income. Alkena and Hsu together earn $84,326 p      Log On


   

Question 111376: I have been struggling with this equation and what I have come up with just does not sound right, could someone help me?
Household Income. Alkena and Hsu together earn $84,326 per year. If Alkena earns $12,468 more per year than Hsu, then how much does each one of them earn per year?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of money Alkena earns, y=amount of money Hsu earns

Since they both make $84,326 a year, this means the sum of their salaries is

x%2By=84326


Also since Alkena makes $12,468 more, this means to find Alkenas salary, simply add 12,468 to Hsu's salary. So this looks like

x=y%2B12468


So that means we have the system


x%2By=84326
x=y%2B12468





%28y%2B12468%29%2By=84326 Plug in x=y%2B12468 into the first equation. In other words, replace each x with y%2B12468. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.



2y%2B12468=84326 Combine like terms on the left side


2y=84326-12468Subtract 12468 from both sides


2y=71858 Combine like terms on the right side


y=%2871858%29%2F%282%29 Divide both sides by 2 to isolate y



y=35929 Divide




Now that we know that y=35929, we can plug this into x=y%2B12468 to find x



x=%2835929%29%2B12468 Substitute 35929 for each y


x=48397 Simplify


So our answer is x=48397 and y=35929



So this means that Alkena makes $48,397 and Hsu makes $35,929