Number- Acres

[Guest]

A rectangular field, the length twice the width, has a surrounding fence. If the posts were placed 16 ft. apart instead of 12 ft., 66 less posts would be needed. Calculate number of acres in the field.

Area = Length x Width

Length = 2W

How do I proceed ?

[Guest]

Please respond. Thanks.

[Guest]

n = number of posts (when spaced 12 ft apart)
L = Length (measured in ft)
W = Width (measured in ft)
P = Perimeter

P = 2L+2W
L = 2W
P/12 = n
P/16 = n-66

Hope this helped,

R. Baber.

[Guest]

That partially helped. I am still unsure how to solve.

[Guest]

6w/16 + 66 = 6w/12

[Guest]

How did you obtain the equation ?

[Guest]

Follow the info in the question

[Guest]

Perimeter is 6w and 66 more for one than in the other

[Guest]

I don't understand 6W is the perimeter.

[Guest]

My attempt:

6W/6 + 66 = 6W/12

6W/16 * 3/3 + 66 * 48 = 6W/12 * 4/4 (48 is LCD)

18W/48 + 3168 + 24/48 = 42W/48 + 3168

42W * 48/48 + 3168 * 48 = 42W + 3168

I don't think that is correct.

[Guest]

Why not start with my equation

[Guest]

I thought I did start with the equation.

My attempt:

6W/6 + 66 = 6W/12 - should be 6W/16 + 66 = 6W/12 (typo)

[Guest]

Please respond. Thanks again.

[Guest]

Solve for w that will be the width

[Guest]

My attempt:

6W/16 + 66 = 6W/12

6W/16 * 3/3 + 66 * 48 = 6W/12 * 4/4 (48 is LCD)

18W/48 + 3168 + 24/48 = 42W/48 + 3168

42W * 48/48 + 3168 * 48 = 42W + 3168

I don't think that is correct.

[Guest]

6W/16 + 66 = 6W/12
Does not imply:
6W/16 * 3/3 + 66 * 48 = 6W/12 * 4/4
which does not imply
18W/48 + 3168 + 24/48 = 42W/48 + 3168
which does not imply
42W * 48/48 + 3168 * 48 = 42W + 3168

None of the steps you did to rearrange and solve the equation make sense. You need to seriously go back and work on fractions and rearranging equations (and maybe also look at "algebraic order of operations"). There is no point attempting questions such as these if you aren't totally comfortable with the basics. Going back and and working on the basics will be more beneficial in the long run.

Your idea to turn everything so that it has denominator 48 is ok. However, the way you executed this idea was wrong.
6W/16 + 66 = 6W/12
6W/16 * 3/3 + 66 * 48/48 = 6W/12 *4/4
18W/48 + 3168/48 = 24W/48
(18W+3168)/48 = 24W/48
Multiplying both sides by 48 gives
18W+3168 = 24W
Subtract 18W from both sides gives
3168 = 6W
Divide both sides by 6
528 = W

Hope this helped,

R. Baber.

[Guest]

Thanks - that helped.

A question:

Why is 6W the perimeter ?

[Guest]

The perimeter of a rectangle is by definition 2L+2W. The question tells you that L = 2W, which means we can replace any occurrence of L with 2W. So the perimeter is therefore 2*2W+2W = 4W+2W = 6W.

Hope this helped,

R. Baber.

[Guest]

That helped. Thanks again.

So, according to the problem, since width = 528 ft., then length is 2 * 528 = 1056 ft.

1056 * 528 = 557568 sq. ft. (area = length * width)

557568 / 43560 (sq. ft. per acre - problem asks how many acres) = 12.8 acres.

Is that correct ?

[Guest]

Yes.......but....6/16 is 3/8.........and 6/12 is 2/8.......rearrange the equation gives 3/8 w - 2/8 w = 1/8 w
So equation becomes w/8 = 66 so w = 66 x 8 = 528........so L is twice that = 1056