Question

The perimeter of a rectangular field is 200 feet. The length of the field is 7 feet more than two times the width of the field.

Part A Write a system of two equations that could be used to find the length and width of the field. Let x represent the length of the field, and let y represent the width of the field.
Part B Solve the system of equations for x and y to determine the dimensions of the field.

Answer 1

x = 2y + 7 ...............(1)
2x + 2y = 200 ........(2)

Substituting the expression for x in equation (1) into equation (2) gives
2(2y + 7) + 2y = 200 .....(3)
Equation (3) simplifies to
6y = 186
Therefore y = 31 feet.
Substituting the value for y into (1) gives
x = 69 feet.