Thread: Functions: How to arrive at the answer?

This is a problem in my book and I don't know how it came to the answer.

A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals.

y[______|______] basically how the figure looks
<--x--> <--x-->

It says to write the area A of the corral as a function of x.

The answer is A=8x(50-x) / 3

I'm confused.

Using the variables, the drawing, and the given total length, find an equation for the total length, in terms of "x" and "y". Solve this equation for y, in terms of x.

Write down the equation for the area A in terms of the lengths x and the depth y. Replace "y" with the expression from above.

If you get stuck, please reply showing your steps and reasoning so far. Thank you!

Here are my steps.

P = 4x + 2y
200 = 4x +2y
y = 200 - 4x / 2
y = 100 - 2x

A = xy
A = x(100 - 2x)

I get stuck after this part. I'm not sure if I need to distribute the x or not.

Originally Posted by Id3aLiStiC

Here are my steps.

P = 4x + 2y
200 = 4x +2y
y = 200 - 4x / 2
y = 100 - 2x

A = xy
A = x(100 - 2x)

I get stuck after this part. I'm not sure if I need to distribute the x or not.

doesn't matter, leave it as is or distribute; it's the same thing.

personally, I'd leave it as is ... it allows me to "see" the value of x that will yield a maximum area.