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

nx-3n-100x-100=0

dx/dt = -250 crates/day

Find dn/dt when x=5 (for 5,000, we'll divide by 1,000 later)

5n-3n-100(5)-100=0

2n-400=0

n=200

Differentiate both sides with repsect to t

(dn/dt)x+ndx/dt-3dx/dt=0

5dn/dt x + ndx/dt-3dx/dt=0

5dn/dt + 3/5(-250)-3(-250)=0

dn/dt = 600/5 = 120

dn/dt = 120/1000 = .12 = change in price