Question 138688

Start with the given system


{{{system(y=x/50+15,y=12500/x)}}}



{{{y=12500/x}}} Now move onto the second equation 



{{{x/50+15=12500/x}}} Plug in {{{y=x/50+15}}}



{{{50x(x/50+15)=50x(12500/x)}}} Multiply both sides by the LCD 50x



{{{x^2+750x=625000}}} Distribute and multiply



{{{x^2+750x-625000=0}}}  Subtract 625000 from both sides. 




{{{(x+1250)(x-500)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x+1250=0}}} or  {{{x-500=0}}} 


{{{x=-1250}}} or  {{{x=500}}}    Now solve for x in each case



So our answer is 

 {{{x=-1250}}} or  {{{x=500}}} 



However, a negative number of jackets does not make sense. So the only solution is {{{x=500}}}



{{{250=12500/500}}} Now plug {{{x=500}}} into the second equation




So our solution is {{{x=500}}} and {{{y=25}}}


So when 500 jackets are sold, the supply will equal the demand at $25.