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# MATH HELP ??

If the supply and demand functions for a commodity are given by

4p − q = 46

and

(p + 2)q = 2,170,

respectively, find the price and quantity that will result in market equilibrium.

equilibrium price $

equilibrium quantity

### 1 Answer

Relevance

- MichaelLv 71 month agoFavourite answer
Supply

4p − q = 46

Solving for q

q = 4p - 46

Demand

(p + 2)q = 2,170

Solving for q

q = 2,170/(p + 2)

------------------------

At equilibrium quantity

4p - 46 = 2,170/(p + 2)

Multiply both sides by p + 2

(4p - 46)(p + 2) = 2170

4p² - 38p - 92 = 2170

4p² - 38p - 2262 = 0

Apply quadratic formula

(work not shown)

p = {-39/2, 29}

The negative price is extraneous

p = 29 <––––– equilibrium price

q = 4p - 46

p = 4(29) - 46

q = 70 <––––– equilibrium quantity

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