Let $x$ represent the price of apples at Farm A, in dollars per pound. So,

$\begin{array}{ccc}5x& =& 8\\ x& =& 1.6\\ 1.6+0.4& =& 2\end{array}$

If we use $x$ to represent the price per pound of Farm B’s apples, we can find the answer by solving the equation $5(x-0.4)=8$ for $x$.

$\begin{array}{ccc}5(x-0.4)& =& 8\\ (x-0.4)& =& 1.6\\ x& =& 2\end{array}$

We know that the artist is making one wreath in the shape of a square. Since a square has four equal sides, we can write the perimeter of the square as:

side times $4$ OR $4s$

The artist is also making a wreath in the shape of a rectangle. The rectangular wreath has a length that is double its width. We can record the perimeter of the rectangle as:

$2(l+w)$

If the length is double the width, then $l=2w,$

which means that:

$P=2(2w+w)$

OR

$P=2\left(3w\right)$

OR

If one side of the square $\left(s\right)$

is 15cm, then the perimeter of the square is:

$\begin{array}{rll}P& =& 4s\\ & =& 4\left(15\right)\\ & =& 60\mathrm{cm}\end{array}$

Recall that the artist wants the rectangular wreath to have the same perimeter as the square wreath (60 cm). For the perimeter of the rectangle:

$\begin{array}{rll}P& =& 6w\\ 60& =& 6w\\ w& =& 10\mathrm{cm}\\ l& =& 2w\\ & =& 2\left(10\right)\\ & =& 20\mathrm{cm}\end{array}$

Therefore, the length of the rectangle will be 20 cm and the width will be 10 cm.

The perimeter of both yards is the same. Therefore, with the geometric symbols indicating identical side lengths, the triangle has a perimeter of 36 metres.

$\begin{array}{rll}36& =& 2x+1+3x+2+2x+1+3x+2\\ 36& =& 10x+6\\ 3& =& x\end{array}$

Fencing required: (subtract $2x+1$)

$\begin{array}{rl}=& 3x+2+2x+1+3x+2\\ =& 8x+5\\ =& 8\left(3\right)+5\\ =& 29 \mathrm{metres}\end{array}$

Fencing costs $100 per metre:

$29\times 100=\$\mathrm{2,900}$

It will cost $2,900 to fence the yards.