Question

mr. cosgrove, a farmer, needs to build a new feed trough for his goats. the trough will be in the shape of a rectangular prism and hold approximately 20 gallons, or 4,620 cubic inches, of food. the height of the trough will be 6 inches so that the goats can access their food easily. mr. cosgrove decides to make the trough 8 times as long as it is wide so all his goats can eat at the same time. which equation can you use to find the width of the feed trough? 4,620w = 8·w·6 4,620 = 8w·w·6 to the nearest tenth of an inch, how wide will the feed trough be? inches wide

Explanation:

Step1: Define variables

Let width = \( w \), length = \( 8w \), height = 6, volume = 4620.

Step2: Volume formula for prism

Volume = length×width×height → \( 4620 = 8w \cdot w \cdot 6 \).

Step3: Solve for \( w \)

Simplify: \( 4620 = 48w^2 \) → \( w^2 = 4620/48 = 96.25 \) → \( w = \sqrt{96.25} \approx 9.8 \).

Answer:

4,620 = 8w·w·6
9.8