A rancher with 750ft of fencing wants to enclose a large rectangle area and then divide it into four equal-sized pens to hold animals. If the maximum area is desired to ensure humane treatment of the anima, what should be the dimensions of the larger rectangle. What should be the dimensions for each of the smaller holding pens?

If a rectangular array,

6x+6y = 750
a = 4xy = 4x(750-6x)/6 = 500x - 4x^2
max area at x = 62.5, y=62.5, large pen = 125x125

If a linear array,
8x+5y = 750
a = 4xy = 4x(750-8x)/5 = 600x - 32/5 x^2
max area at x=46 7/8, y=75, large pen = 186.5x75

As usual, the square provides the largest area.

As usual, in either case, the fence is evenly divided among lengths and widths.

the average of five numbers is 16. Suppose 10 is added to five numbers. What is the average of the six numbers?

Do not tag a new question at the end of somebody else's question.

It will appear to be a reply to that problem

Yours:
The sum so far is 80
after adding 10 the new sum is 90
avg of those 6 numbers = 90/6 = 15

To find the dimensions of the larger rectangle, we can use the fact that the perimeter of a rectangle is equal to two times the length plus two times the width.

Let L be the length of the larger rectangle, and W be the width of the larger rectangle. The perimeter is then given by:

2L + 2W = 750

We need to divide this larger rectangle into four equal-sized pens. Since we want to maximize the total area of the pens, each pen should be a square.

Let S be the side length of each smaller pen. Since there are four pens, each with a width of S, the width of the larger rectangle is equal to four times the width of a smaller pen:

W = 4S

Substituting this into the previous equation, we have:

2L + 2(4S) = 750
2L + 8S = 750

Now we have two equations and two variables (L and S). Solving this system of equations will give us the dimensions of the larger rectangle and the smaller pens.

To solve these equations, we need to know whether you want the dimensions in terms of the length of the side of the smaller pen (S) or in terms of the measurements in feet.