The town swimming pool is d feet deep. The width of the pool is 5 feet greater than 5 times its depth. The length of the pool is 50 feet greater than 5 times its depth. Enter a simplified expression to represent the volume of the pool.
Accepted Solution
A:
Answer:[tex]V = 25d ^ 3 + 275d ^ 2 + 250d[/tex]Step-by-step explanation:If the pool has a rectangular shape then its volume can be written as:V = Width * Length * DepthLet's call:w = widthl = lengthd = depth.So we know from the statement of the problem that:[tex]d = d[/tex][tex]w = 5 + 5d[/tex] (5 feet more than 5 times the depth)[tex]l = 50 + 5d[/tex] (50 feet more than 5 times the depth)Then, the volume can be written according to the depth as:[tex]V = d(5 + 5d)(50 + 5d)[/tex][tex]V = d[250 + 25d + 250d + 25d ^ 2][/tex][tex]V = 25d ^ 3 + 275d ^ 2 + 250d[/tex]