The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136 m. Find the width and the length Part A: What does the independent variable represent?

Part B: What is the mathematical statement?

Part C: What is the value of the independent variable?

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Step-by-step explanation:

Represent the width by W.  Then, "The length of a rectangular field is 7 m less than 4 times the width" expressed symbolically is

L = 4W - 7 (dimensions in meters)

Recall that the perimeter formula in this case is P = 2L + 2W, and recognize that the perimeter value is 136 m.  After substituting 4W - 7 for L, we get:

136 m = 2(4W - 7) + 2W, or

136 = 8W - 14 + 2W, or

150 = 10W        These three equations are equivalent mathematical statements.

150 = 10W reduces to W = 15 (meters).

Part A:  the independent variable is W, the width of the field.

Part B:  The mathematical statement is 136 m = 2(4W - 7) + 2W, which after algebraic manipulation becomes 150 = 10W.

Part C:  The above equation can be solved for W:  W = 15 meters.  This is the value of the independent variable.

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