Problema Solution
A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 feet, and the distance around should be no more than 380 feet.
a. Write a system of inequalities that models the possible dimensions of the garden.
Answer provided by our tutors
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:
, which can be simplified by dividing with 2:
, and if you want to separate Y from the numbers
.
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 . 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).