SOLUTION: Could someone please help me with this tricky word problem??? The demand and supply equations for a certain item are given by {{{D=-5p+40}}} {{{S=-p^2+30p-8}}} Find the equilib

Question 103995: Could someone please help me with this tricky word problem???
The demand and supply equations for a certain item are given by

Find the equilibrium price.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the equilibrium price, set the two equations equal to one another

Add 5p to both sides

Subtract 40 from both sides

Combine like terms

Let's use the quadratic formula to solve for p:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-1, b=35, and c=-48

Square 35 to get 1225

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our possible solutions are:
or

However, plugging in results in a negative demand. So the only solution is . So the equilibrium price is about $1.43
RELATED QUESTIONS
The demand and supply equations for a certain item are given by {{{D=-5p+40}}}... (answered by jim_thompson5910)

HELP! I need assistance with this demand supply problem! The demand and supply... (answered by Edwin McCravy)

Could someone please help me solve this word problem? The demand equation for a... (answered by edjones)

Could you help me with this problem? The demand and supply equations for a certain... (answered by edjones)

The demand and supply equations for a certain item are given by D=-5p+40 S=-p^2+30p-8 (answered by stanbon)

Please help! The demand and supply equations for a certain item are given by: D= -5p... (answered by stanbon,scott8148)

Hi: I have this word problem that I'm uncertain how to set up to solve. If someone... (answered by ankor@dixie-net.com)

This ? is hard please help? The demand and supply equations for a certain item are... (answered by jim_thompson5910)

The demand and supply equations for a certain item are given by D = 5p + 40 S= -p^2 +... (answered by ankor@dixie-net.com)