Please Help - Basic Calculus Word Problem...

Question

A bazaar is supplied n thousands of crates of apples daily when it is sold at x pesos per crate and the supply equation is

xn - 3x -100x -100 = 0,

If the supply daily is decreasing by 250 crates a day, at what rate is the price changing when the daily supply is 5000 crates?

Answer 1

From your equation xn-103x = 100 implies that x = 100/(n-103). Differentiating both sides implicitly you get:

x(dn/dt) +n(dx/dt) - 103 = 0. dx/dt is given at -250, and you then sub in 100/(n-103) for x resulting in

5000*dx/dt = 25000/(5000-103). Solve for dx/dt.