Agriculture A farmer grows tomatoes and cucumbers in the field shown. The annual cost

of growing tomatoes is \(.27 per square foot. The annual cost of growing cucumbers is \).10 per square foot. Let x represent the width (in feet) of the tomato portion of the field.

1. In terms of x, what is the area of the tomato portion? of the cucumber portion?
2. Write and simplify an expression in terms of x for the annual cost of growing both crops.
3. Find the annual cost of growing both crops if the width of the tomato portion is 350 feet
4. 
   

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property: $a\left(b+c\right)=a·b+a·c$

The tomato and cucumber portions have dimensions as shown in figure,

Formula:

Area$=$Length $\times$Breadth

The length of tomato is $500$ft

And its breath is $x$ft.

So, the area of the tomato is $500x$ft.

The length of the cucumber is $500$ft.

And its breath is $=(800-x)$ft.

So, the area of the cucumber is $=500(800-x)$square ft.

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property: $a\left(b+c\right)=a·b+a·c$

Annual cost of growing tomatoes and cucumber is $\$·27$and $\$·10$

As found in part (a), the areas of tomatoes and cucumber portions are $500x$square feet and $500(800-x)$square feet respectively.

So, the annual cost of growing both crops is

$\begin{array}{l}\$(0\cdot 27)\left(500x\right)+\$(0\cdot 10)\left(500\right(800-x\left)\right)\\ =\$135x+\$50(800-x)\\ =\$135x+\$(40000-50x)\\ =\$(135x+40000-50x)\\ =\$(85x+40000)\end{array}$

In an algebraic expression, terms are separated by plus or minus signs.

The term coefficient refers to the number in front of the variable in any term of the expression.

A constantterm is the number which have no variable associated with it.

Like terms are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property: $a\left(b+c\right)=a·b+a·c$

Width of tomato portion $x=350$ft .

As found in part (b),

The annual cost is given by $\$(85x+40000)$

Thus for $x=350$ft

The annual cost $=\$(85\times 350+40000)$

$\begin{array}{l}=\$(29750+40000)\\ =\$69750\end{array}$