1. ## Algebra problem!

I'm working from a book called Mathematics for Economics and Finance (Martin Anthony and Norman Biggs) I have a problem with one of their damn examples on supply and demand.

the supply set is S={(p,q)|q=bp-a} and D={(p,q)|q=c-dp}

when an excise tax is imposed i need to find the equilibrium quantity ()

this is found by finding the equilibrium price ()

So I solve simultaneously and get:

which is in the book. Now I need to find qT which the book states is found by:

I can't figure out how the hell these people managed to get bc-ad as the numerator for the first term, Can someone tell me how they got this!?

2. $q^T = c - d\left(\dfrac{c+a}{b+d} + \dfrac{bT}{b+d}\right)$

$= c - \dfrac{dc+da}{b+d} - \dfrac{bdT}{b + d}$

$= \dfrac{bc + dc}{b + d} - \dfrac{dc+da}{b+d} - \dfrac{bdT}{b + d}$

$= \dfrac{bc + dc - dc - da}{b + d} - \dfrac{bdT}{b + d}$

$= \dfrac{bc - da}{b + d} - \dfrac{bdT}{b + d}$

3. This problem was also posted in the "algebra and prealgebra" section.