Question

Would someone help me solve this question? You have 1200 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?

Answer 1

I'm slightly confused with the wording of the problem, but I believe the first thing that you need to do is create an equation. What do you think it would be?

Answer 2

@1lorax2 The equation I came up with is 3x + 2y = 1200.
I then am looking to make a y = equation
So after subtracting 3x on both sides an dividing by 2
I got
y = 1200-3x/2
I am confused with Area = xy
which would be my next step

Answer 3

Ok, I'm kind of confused myself. Maybe if we work it similar to a system of equations.... If that were the case, you would now replace the y in the equation with (1200-3x)/2, for an equation of 3x+2((1200-3x)/2)=1200, and solve for x, which would theoretically allow you to multiply x and y for your area.... But based on the numbers, I kind of doubt it. I'm sorry! Honestly, guess and check might not be a bad option.... do you have any answer choices?

Answer 4

@1lorax2 Unfortunately I don't have any answer choices. I appreciate your help though!
I will do some guessing and checking!

Answer 5

Ok! If you want, I can help with that. The original equation would still need to be true, I just have no idea how to solve for x or y.

Answer 6

@1lorax2 Thank you!
I need to have Area =xy.
I already have what y equals.
So A=x(1200-3x/2)
My problem actually lies in solving this equation.
I am not sure what to do first, divide the numbers in the equation by 2 or distribute x throughout my parenthesis.

Answer 7

If it were me, I would distribute first.

Answer 8

This is what I came up with

@1lorax2

Answer 9

That all looks good, except for in the last line, it should be -1 and 1/2x^2

Answer 10

@1lorax2 Okay so the mixed number 1 and 1/2 would equal 1.5 essentially, correct?

Answer 11

Right!

Answer 12

So if \[a = 600x - 1.5x ^{2}\]

Answer 13

I think so.......... I'm honestly lost right now. I'm so sorry I'm not more help!

Answer 14

@1lorax2 I need to find the vertex.
So my equation would look something like
\[x = -b \div 2a\]
\[-600\div2(1.5) \]
Then my x = 200.
Right?

Answer 15

@1lorax2
Don't worry, I really appreciated all your help, I think I have it from here. You really helped me get through the part I was struggling with. Thank you so much, have a nice night!

Answer 16

You too! Good luck!!