story problem: average distance of earth from the sun

[bandaidgirl]

For each planet our solar system, its year is the time it takes the planet to revolve once around the sun. The formula "E = 0.2x^3/2" models the number of earth days in a planet's year, E, where x is the average distance of planet from the sun, in millions of kilometers. Use the formula to solve.

We have 365 earth days in our year. What is the average distance of earth from the sun?


I have:

365=0.2x^3/2
------------------
0.2 0.2

1825=x^3/2
1825^2/3=(x^3/2)^2/3
1825^2/3=x

the book say the answer is x=140 how do you come up with that

 

[Denis]

Re: story problem

for each planet our solar system, its year is the time it takes the planet to revolve once around the sun. the formula
E=0.2x^3/2

That's incorrect; you need brackets: E = .2x^(3/2) : not .2x^3 divided by 2.

i have
365=0.2x^3/2
------------------
0.2 0.2
1825=x^3/2
1825^2/3=(x^3/2)^2/3
1825^2/3=x
the book say the answer is x=140 how do you come up with that

x = 1825^(2/3) is correct.
If book says answer is 140, then book is wrong; rounded, answer is 149.
How? Use your calculator.