Perimeter of soccer field is 430 yards. Length is 40 yards less than twice the width what are the dimensions

Question

perimeter story problem

Answer 1

P = 2L + 2W

430 = 2L + 2W

 

L = 2W - 40

The length is 40 less than 2 times the width.

 

Make a system:

430 = 2L + 2W

L = 2W - 40

 

Substitute L for 2W - 40 in the original equation. Then simplify and solve for W:

430 = 2(2W - 40) + 2W

430 = 4W - 80 + 2W

430 = 6W - 80

+80         + 80

510 = 6W

85 = W

 

Substitute 85 for W into one of the equations and solve for L:

L = 2(85) - 40

L = 170 - 40

L = 130

 

Dimensions are L = 130 yds and W = 85 yds.

 

Answer 2

Let the width = W

We are told that the length is 40 less (-40) than twice the width (2W)

So let the Length = 2W-40

 

Now solve for W.

We know the perimeter is adding all 4 sides, so we have to double the width and length.

 

Equation should look like this

 

2(2W-40) + 2(W) = 430

 

4W-80+2W=430

 

6W-80=430

 

6W=510

 

W=85

 

Now answer the questions by plugging back in.

 

The width is 85

The length is 2(85)-40

The length is 130

 

Test is to make sure it works...130+130+85+85=430

Problem solved