A farmer has 165 feet of fencing material in which to enclose a rectangle area. He wants the length x to be greater than 50 feet and width y to be no more than 20 feet. write a system to represent this situation.
a farmer has 165ft of fencing material in which to enclose a rectangular grazing area. he wants the length x to be greater than 50 and the width y to be no more than 20ft. write a system to represent this situation?
To represent this situation, we can set up the following system of inequalities:
1) The perimeter of the rectangle is equal to 165 feet:
2x + 2y = 165
2) The length x is greater than 50 feet:
x > 50
3) The width y is no more than 20 feet:
y <= 20
Combining all of these equations, the system becomes:
2x + 2y = 165
x > 50
y <= 20
To write a system of equations that represents this situation, we need to consider the constraints given:
1. The length, x, must be greater than 50 feet.
2. The width, y, must be no more than 20 feet.
3. The perimeter of the rectangle formed by the fencing material must be equal to 165 feet.
Let's define the variables:
x = length of the rectangle
y = width of the rectangle
Based on the constraints, we have the following system of equations:
Equation 1: x > 50
This equation represents the first constraint that the length, x, must be greater than 50 feet.
Equation 2: y <= 20
This equation represents the second constraint that the width, y, must be no more than 20 feet.
Equation 3: 2x + 2y = 165
This equation represents the third constraint that the perimeter of the rectangle formed by the fencing material must be equal to 165 feet. Since we are using the whole amount of fencing material, we need to consider both sides of the rectangle as well as both the top and bottom sides.
Therefore, the system of equations is:
x > 50
y <= 20
2x + 2y = 165
Let x=length, y=width.
"A farmer has 165 feet of fencing material in which to enclose a rectangle area." means
2(x+y)≤165 ....(1)
"He wants the length x to be greater than 50 feet" means
x>50 ......(2)
"and width y to be no more than 20 feet." means
y&le=20....(3)
The system is the collection of inequalities (1) to (3).