Mathematics, 02.07.2019 09:30 NotYourStudent
The price p of a good and the quality q of a good are linked. the demand for a new pair of trainers can be modelled using the equation p= (-3/4)q+35 the supply of trainers can be modelled using the equation p= (2/3)q+1. they meet on the same pair of axes. the equilibrium point is the point whereto supply and demand lines meet find the values of p and q at the equilibrium point.
Answers: 1
![\bf \stackrel{\textit{Supply}}{-\cfrac{3}{4}Q+35}~~=~~\stackrel{\textit{Demand}}{\cfrac{2}{3}Q+1}\implies \stackrel{\textit{multiplying by 12}}{12\left( -\cfrac{3}{4}Q+35 \right)=12\left( \cfrac{2}{3}Q+1 \right)} \\\\\\ -9Q+420=8Q+12\implies 408=17Q\implies \cfrac{408}{17}=Q\implies \boxed{24=Q} \\\\\\ \stackrel{\textit{using the found Q in the Demand equation}}{P=\cfrac{2}{3}(24)+1}\implies P=16+1\implies \boxed{P=17} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{Equilibrium}{(24,17)}~\hfill](/tpl/images/0042/0789/082a9.png)
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