Demand for goods of an industry is given by the equation p×q=100 & supply is given by the equation 20+3p=q were p is the price and q is the quantity. Find price and quantity in quadratic form
To find the equilibrium price and quantity in quadratic form, we need to solve the equations for the demand and supply.
Given that the demand equation is p*q = 100 and the supply equation is 20 + 3p = q, we can substitute the value of q from the supply equation into the demand equation to get a quadratic equation in terms of p.
Let's start by rearranging the supply equation to solve for q:
q = 20 + 3p
Now substitute this expression for q in the demand equation:
p * (20 + 3p) = 100
Simplify the equation:
20p + 3p^2 = 100
Rearrange the equation to form a quadratic equation:
3p^2 + 20p - 100 = 0
Now we have a quadratic equation in terms of p. To solve for p, we can use the quadratic formula:
p = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = 20, and c = -100. Substituting these values into the quadratic formula, we get:
p = (-20 ± √(20^2 - 4 * 3 * -100)) / (2 * 3)
Simplifying the equation further:
p = (-20 ± √(400 + 1200)) / 6
p = (-20 ± √1600) / 6
p = (-20 ± 40) / 6
This gives us two possible values for p:
1. p = (-20 + 40) / 6 = 20 / 6 = 10 / 3
2. p = (-20 - 40) / 6 = -60 / 6 = -10
Since price cannot be negative, we can disregard the second solution.
So, the equilibrium price (p) in quadratic form is p = 10/3.
To find the quantity (q), we can substitute the value of p into the supply equation:
q = 20 + 3p
q = 20 + 3(10/3)
q = 20 + 10
q = 30
Therefore, the equilibrium quantity (q) in quadratic form is q = 30.