Thread: Nonlinear Systems

I am working on some homework solving nonlinear equations and the word problems are giving me a little difficulty. If someone could help me understand how to set up a system of equations for these problems, it would really help me.
Here a couple examples:
1) Dividing a pasture.
The area of a rectangular pasture is 8750 square feet. The pasture is divided into three smaller pastures by two fences parallel to the shorter sides. The widths of two of the larger pastures are the same, and the width of the third is one-half that of the others. Find the dimensions of the original pasture if the perimeter of the smaller of the subdivisions is 190 feet.
2) Carpet sale.
A salesperson sold a square carpet and a rectangular carpet whose length was 6 feet more than its width. The combined area of the two carpets was 540 square feet. The price of the square carpet was $12 per square yard, and the price of the rectangular carpet was $10 per square yard. If the salesperson received $50 more for the rectangular piece, find the dimensions of each carpet.

Let the length of the pasture be L, and th width w. So wL = 8750.
Now draw yourself a picture. Let the width of th larger sub-pasture be s. Then 2.5s = L.
Also, in the smaller sub-pasture we have s+2L=190.

So we have three variables and three equations:
wL = 8750
2.5s = L
s+2L = 190

You will see that you can use the last two equations to find s and L, and then you can find w:
2.5s = L so:
s + 2L = s + 2(2.5L) = 6s = 190
s = 190/6
L = 2.5s = 2.5(190/6)

Finally:
wL = 8750
w = 8750/L etc. you can finish it off.

The numbers look a bit odd to me, so please check I haven't made any silly mistakes.

The second question can be done similarly; try it yourself, and ask if you get stuck.