The supply and demand equations for a small LCD television are given by $\left\{ \begin{array} { l l }
p + 0.6 x = 1436 & \text { Demand } \
p - 0.2 x = 300 & \text { Supply }
\end{array} \right.$ where $p$ is the price (in dollars) and $x$ represents the number of televisions. For how many units will the quantity demanded equal the quantity supplied? What price corresponds to this value?
A)1795 units at $359.00
B)2170 units at $134.00
C)1420 units at $134.00
D)2170 units at $584.00
E)1420 units at $584.00

Question

The supply and demand equations for a small LCD television are given by $\left\{ \begin{array} { l l } 
p + 0.6 x = 1436 & \text { Demand } \
p - 0.2 x = 300 & \text { Supply }
\end{array} \right.$ where $p$ is the price (in dollars) and $x$ represents the number of televisions. For how many units will the quantity demanded equal the quantity supplied? What price corresponds to this value?
A)1795 units at $359.00
B)2170 units at $134.00
C)1420 units at $134.00
D)2170 units at $584.00
E)1420 units at $584.00

Quizplus · Accepted Answer

To find the equilibrium point where quantity demanded equals quantity supplied, we set the two equations equal to each other and solve for $x$:$$p + 0.6x = 1436$$$$p - 0.2x = 300$$Subtracting the second equation from the first gives:$$0.8x = 1136$$Solving for $x$ gives:$$x = \frac{1136}{0.8} = 1420$$To find the corresponding price $p$, substitute $x = 1420$ into either of the original equations. Using the supply equation:$$p - 0.2(1420) = 300$$$$p = 300 + 0.2(1420) = 300 + 284 = 584$$Therefore, the equilibrium occurs at 1420 units at a price of $584.

The Supply and Demand Equations for a Small LCD Television {p+0.6x=1436 Demand p−0.2x=300 Supply \left\{ \begin{array} { l l } p + 0.6 x = 1436 & \text { Demand } \\p - 0.2 x = 300 & \text { Supply }\end{array} \right.{p+0.6x=1436p−0.2x=300​ Demand Supply ​

The Supply and Demand Equations for a Small LCD Television $\left\{ \begin{array} { l l } p + 0.6 x = 1436 & \text { Demand } \\p - 0.2 x = 300 & \text { Supply }\end{array} \right.$