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.
a. y>=110
2x+2y<=380
b. y>=110
2x+2y>=380
c. y<=110***
2x+2y<=380***
d. y<=110
2x+2y>=380
"at least" means >=
care to change your answer?
The correct answer is:
a. y>=110
2x+2y<=380
The correct system of inequalities that models the possible dimensions of the garden is:
a. y >= 110 (The length of the garden should be at least 110 ft.)
2x + 2y <= 380 (The distance around should be no more than 380 ft.)
The first inequality, y >= 110, represents that the length of the garden must be greater than or equal to 110 ft. This makes sense since the problem states that the length should be at least 110 ft.
The second inequality, 2x + 2y <= 380, represents the perimeter constraint. The distance around the garden should be no more than 380 ft. The equation is expressed as 2x + 2y because we need to account for both the length and width of the garden in the perimeter calculation.
Therefore, the correct answer is option A: y >= 110 and 2x + 2y <= 380.