Homework Help: math

Posted by Jane on Thursday, December 29, 2011 at 1:40pm.

A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft. Write a system of inequalities that models the possible dimensions of the garden. Graph the system to show all possible solutions.

math - Reiny, Thursday, December 29, 2011 at 4:21pm
let the length be x
let the width be y
so 2x + 2y < 380
x + y < 190

also x > 110

to graph:
draw a vertical line (dotted) at x = 110
shade in the region to the right of that line

draw the line x+y = 190 , use the intercepts, its easy that way
shade in the region below that line

The region shaded between the two lines and above the x-axis represents your solution. Any point in that region satisfies both conditions.
I suggest using 1 unit on your grid to be 50 ft
math - Henry, Thursday, December 29, 2011 at 5:32pm
Given: L >= 110 Ft., P <= 380 Ft.

P = 2W + 2*110 <= 380,
2W + 220 <= 380,
2W <= 380 - 220,
2W <= 160,
W <= 80 Ft.

2L + 2W <= 380,
Divide both sides by 2:
L + W <= 190,
Let: L = Hor., W = Ver.
L + W <= 10. Scale factor = 19.
Actual values obtained by multiplying by 19.
Graph: L + W = 10, The boundary line.
(L,W).
(0,10) = (0,190)
(10,0) = (190,0).

All points on and below the boundary
line will satisfy the inequality.
Use the coordinates to the rt of = sign for L + W <= 190.

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