SOLUTION: The demand equation is given as {{{y=x/50+15}}} and the supply as {{{y=12500/x}}}. Find the equilibrium price.

Algebra ->  Graphs -> SOLUTION: The demand equation is given as {{{y=x/50+15}}} and the supply as {{{y=12500/x}}}. Find the equilibrium price.      Log On


   

Question 138688: The demand equation is given as y=x%2F50%2B15 and the supply as y=12500%2Fx. Find the equilibrium price.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system

system%28y=x%2F50%2B15%2Cy=12500%2Fx%29


y=12500%2Fx Now move onto the second equation


x%2F50%2B15=12500%2Fx Plug in y=x%2F50%2B15


50x%28x%2F50%2B15%29=50x%2812500%2Fx%29 Multiply both sides by the LCD 50x


x%5E2%2B750x=625000 Distribute and multiply


x%5E2%2B750x-625000=0 Subtract 625000 from both sides.



%28x%2B1250%29%28x-500%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x%2B1250=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%2F500 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.