Calculus problem for my youngest son!

Question

A store is given n thousands of crates of lemons daily when it is sold at c pesos per crate and the supply equation is

cn - 3c - 100n - 100 = 0

If the day by day supply is diminishing by 250 crates each day, at what rate is the price changing when the day by day supply is 5000 crates?

Answer 1

dn/dt = -0.25 and n = 5

We need dc/dt

Differentiate implicitly

cn - 3c - 100n - 100 = 0

c dn/dt + n dc/dt - 3 dc/dt - 100 dn/dt = 0

When n = 5, 5c - 3c - 500 - 100 = 0, so 2c = 600 so c = 300

So substituting in :

300 x -0.25 + 5 dc/dt - 3 dc/dt - 100 x -0.25 = 0

So -75 + 2 dc/dt + 25 = 0

2 dc/dt = 50

dc/dt = 25 pesos per crate per day