In the pair of supply and demand equations below, x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price. p = 47 - 3x2 and p = x2 + 12x + 31 equilibrium quantity thousand units equilibrium price dollars
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Determining Equilibrium in Supply and Demand Equations
In this problem, you are provided with a pair of supply and demand equations. Here, \( x \) represents the quantity demanded in units of a thousand, and \( p \) represents the unit price in dollars. The task is to find the equilibrium quantity and the equilibrium price.
The supply and demand equations are:
\[ p = 47 - 3x^2 \]
\[ p = x^2 + 12x + 31 \]
**Equilibrium Status:**
- **Equilibrium Quantity:** ____ thousand units
- **Equilibrium Price:** ____ dollars
At equilibrium, the quantity demanded and the quantity supplied are equal, and they meet at a specific price point. To find the equilibrium, you need to set the two equations equal and solve for \( x \). Once \( x \) is identified, substitute it back into either equation to find the corresponding price \( p \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad356ace-94cd-4e8a-aa7f-bdf17308114e%2F7f0b5c19-5b90-46f0-9623-e10b32e7af0e%2Fxksijqf.png&w=3840&q=75)
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