6. the demand equation for primo earbuds is $p = -\frac{1}{50}x + 40$, where $x$ is the quantity demanded…

6. the demand equation for primo earbuds is $p = -\frac{1}{50}x + 40$, where $x$ is the quantity demanded per week and $p$ is the unit price in dollars. the supply equation for primo earbuds is $p=\frac{1}{25}x + 10$, where $x$ is the quantity supplied per week and $p$ is the unit price in dollars. determine the equilibrium quantity and equilibrium price. include units with your answers. equilibrium quantity: equilibrium price:

6. the demand equation for primo earbuds is $p = -\frac{1}{50}x + 40$, where $x$ is the quantity demanded per week and $p$ is the unit price in dollars. the supply equation for primo earbuds is $p=\frac{1}{25}x + 10$, where $x$ is the quantity supplied per week and $p$ is the unit price in dollars. determine the equilibrium quantity and equilibrium price. include units with your answers. equilibrium quantity: equilibrium price:

Answer

Explanation:

Step1: Set demand equal to supply

Set $-\frac{1}{50}x + 40=\frac{1}{25}x+10$.

Step2: Solve for x (equilibrium quantity)

First, move the x - terms to one side: $-\frac{1}{50}x-\frac{1}{25}x=10 - 40$. Find a common denominator for the x - terms. Since $\frac{1}{25}=\frac{2}{50}$, we have $-\frac{1}{50}x-\frac{2}{50}x=- 30$. Combining like - terms gives $-\frac{3}{50}x=-30$. Multiply both sides by $-\frac{50}{3}$: $x = 500$ units.

Step3: Solve for p (equilibrium price)

Substitute $x = 500$ into the supply equation $p=\frac{1}{25}x + 10$. $p=\frac{1}{25}\times500+10$. $p = 20 + 10=30$ dollars.

Answer:

Equilibrium Quantity: 500 units Equilibrium Price: 30 dollars