SOLUTION: 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. a.) Wri

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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. a.) Wri      Log On


   

Question 288212: 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.
a.) Write a system of inequalities that models the possible dimensions of the garden.
b.) Graph the system to show all possible solutions
Answer by amnd(23) About Me  (Show Source):
You can put this solution on YOUR website!
a) The distance around a rectangle would be 2X + 2Y, with X = length and Y = width.
We know that X = 110, so the distance around would be 220 + 2Y. Since this value cannot be more than 380 ft (or, "is less or equal to" 380 ft), we can write it as this inequality system:
220+%2B+2Y+%3C=+380, which can be simplified by dividing with 2:
110+%2B+Y+%3C=+190, and if you want to separate Y from the numbers Y%3C=80
.
b) This would simply yield a straight line on 80, and since I assume that Y > 0 (or else we wouldn't have a garden!), the possible solutions would be between 0 and 80 (the inequality system would be 0+%3C+Y+%3C=+80. The line Y = 0 should be dashed (since Y > 0) while Y = 80 should be a full line (since it's "less or EQUAL to"). Shade in the area between these two lines (or you can draw in X = 110, and this would yield a single line containing possible values for Y between 0 and 80).
I hope this is understandable :)