Question

A farmer plans to create a rectangular garden that he will enclose with chicken wire. The garden can be no more than 30 ft wide. The farmer would like to use at most 180 ft. of chicken wire. Write a system of linear inequalities that models this situation.

Answer 1

@jim_thompson5910, Can you help me

Answer 2

Let L = length and W = width

Answer 3

"The garden can be no more than 30 ft wide" what does that translate into?

Answer 4

30 + x = w

Answer 5

Is that right @jim_thompson5910

Answer 6

30 + x =w @jim_thompson5910

Answer 7

"The garden can be no more than 30 ft wide" means that

\(\Large w \le 30\)

Answer 8

@jim_thompson5910. Is that the answer

Answer 9

no, that's one part of the answer

Answer 10

"Write a system of linear inequalities" implies there is more than one inequality

Answer 11

Oh so how would i find the other part

Answer 12

how would translate

"The farmer would like to use at most 180 ft. of chicken wire"

?

Answer 13

F less than 180 ?

Answer 14

Say P is the perimeter, so if "The farmer would like to use at most 180 ft. of chicken wire", then

\(\Large P \le 180\)

The perimeter P is

P = 2L + 2W, so we can replace the P in the inequality with 2L + 2W to get

\(\Large 2L + 2W \le 180\)

\(\Large 2(L + W) \le 180\)

\(\Large L + W \le \frac{180}{2}\)

\(\Large L + W \le 90\)


see how I'm getting all this?

Answer 15

Yes...

Answer 16

any questions on it?

Answer 17

i noticed you were typing, but you stopped

Answer 18

Sorry my computer died. Now im using my phone. Yes i get it. And would those other ones work for the question @jim

Answer 19

The final answer would be

\(\Large W \le 30\)
\(\Large L + W \le 90\)
\(\Large L > 0\)
\(\Large W > 0\)

I'm adding those last two inequalities because I'm forcing the length and width to be positive numbers

Answer 20

So the final answer is a combination of what is discussed above

Answer 21

@jim_thompson5910, Thank you so much, i can not thank you enough!

Answer 22

you're welcome