Question

A farmer has a rectangular garden plot surrounded by 200 ft of fence. find the length and width of the garden if its area is 2400 ft squared.
Ok So i got the answer which is 60x40 heres my work:
2L+2W=200
L+W=100 What im wondering is where did this come from my friend helped me with this part i dont get it?!?!
ETC

Answer 1

You are on the right track. You want to get that relation:

L + W = 100

because that leads to:

W = 100 - L

and now you can get an equation for the area that is in one independent variable:

A = L x W = L x (100 - L)

A = 100L - L^2 = 2400

See how we are working with just "L" for an independent variable now instead of both W and L? That's the whole key. And now you simply solve the quadratic equation for "L". Do you need help with that step?

Answer 2

Where did the L+W=100 come from though??

Answer 3

rather 2L+2W=200

Answer 4

Well, we know that 2L + 2W is the perimeter and that is 200 because we have 200 ft of fencing. So,

2L + 2W = 200

and just divide both sides by 2.

Answer 5

You would solve:

L^2 - 100L + 2400 = 0

(L - 60)(L - 40) = 0

L would be 60 (not 40) because L would be the longer dimension, saving 40 for the W.

Answer 6

Ok I get it now!!

Answer 7

may you help me with one more?

Answer 8

It's a bit tricky, but doing this one will open up understanding on how to do other problems. Good luck in all of your studies and thx for the recognition! Sure, I'l try one more but then I have to go.

Answer 9

okay! thanks : What quantity of a 60% acid solution must be mixed with a 30% solution to produce 300 ml of a 50% solution.
I just dont get what is being asked in the questions it is really confusing me

Answer 10

This one is a little harder, but I'll be able to do it. More importantly, I'm shooting for you to understand it.

Answer 11

ok

Answer 12

I'm sorry, I have to go. Emergency at home.

Answer 13

Let x = ml of the 60% solution and let y = ml of the 30% solution.

x + y = 300

The 300 ml is at 50% strength, so wthis is the same as 150 ml of 100% solution. So our second equation is:

(0.60)x + (0.30)y = 150

If you solve those 2 simultaneous equations in 2 variables, you will get :

x = 200 and y = 100.

To check this answer:

200 + 100 = 300

and

(0.60)(200) + (0.30)(100) = 150