Solve Problems Using Systems of Linear Equations
-As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The weekly supply and demand models for a certain type of television are as follows:
Demand: $\mathrm { N } = - 3 \mathrm { p } + 780$
Supply: $\quad N = 2.5 p$
where $\mathrm { p }$ is the price in dollars per television.
Find the price at which supply and demand are equal. At this price, how many televisions can be supplied and sold each week?
A) $\$ 141.82 ; 355$
B) $\$ 1560.00 ; 3900$
C) $\$ 310.80 ; 777$
D) $\$ 141.82 ; 362$

Question

Quizplus · Accepted Answer

To find the price at which supply equals demand, set the demand equation equal to the supply equation: $-3p + 780 = 2.5p$. Solving for $p$ gives $p = 141.82$. Substituting $p = 141.82$ into either equation (for simplicity, use the supply equation) gives $N = 2.5 \times 141.82 = 354.55$, which rounds to 355 televisions.

Solve Problems Using Systems of Linear Equations -As the Price N=−3p+780\mathrm { N } = - 3 \mathrm { p } + 780N=−3p+780

Solve Problems Using Systems of Linear Equations
-As the Price $\mathrm { N } = - 3 \mathrm { p } + 780$