Final answer:
The width of a rectangular pan with an area of 150 square inches and a length that is 2/3 the width is found to be 15 inches.
Step-by-step explanation:
The question asks us to find the width of a rectangular pan given that its length is 2/3 the width and its area is 150 square inches. Let's denote the width of the pan as w inches. Therefore, the length of the pan can be expressed as (2/3)w inches.
The area (A) of a rectangle is calculated by multiplying the width by the length. In equation form, we have: A = w × (2/3)w. Substituting the given area, 150 square inches, into the equation gives us 150 = w × (2/3)w.
To solve for the width, we first expand the equation:
150 = (2/3)w^2. To isolate w^2, we multiply both sides of the equation by 3/2 which gives us 225 = w^2. Taking the square root of both sides, we get w = 15 inches, which matches option C.
Therefore, the width of the pan is 15 inches.