Please help - Applied Calc question needs answer ASAP!?

Question

Given the supply and demand functions D(x) = 15-1/3x and S(x) = 2x^1/3, find the equilibrium point.

I set the two equal to each other and cannot seem to get the correct answer no matter how I solve it!

Sorry, the demand function is D(x) = 15 - (1/3)x and the supply function is S(x) = 2 * x^(1/3).

Thanks guys! 27 is the correct answer! I just needed a means to figure out how to get it! Thanks again! :)

Answer 1

Setting
S(x) = D(x) and eliminating fractions gives

2x^(1/3) + x/3 -15 = 0

Now you could let u = x^(1/3) so u^3 = x which gives you a cubic equation .

But before doing that, let's hope the solution is an easy one. Since the first term is just 2 times the cube root of x let's try some perfect cubes such as 1, 8, 27, 64, etc as see if by chance one of them is the solution.

Trying 8 gives 2cuberoot(8) + 8/3 -15 which does not equal zero. Trying 27 gives

2 cuberoot(27) + 27/3 - 15 which (check it out) does equal zero.

So by substitution of perfect cubers we found the solution is

x = 27.

The formula to solve cubics is difficult. Higher degree equations can only be solved by guessing methods similar to what we did here.

Answer 2

Check the Demand function. Is it 15-(x/3) or 15- 1/(3x)