Word Problems
Dimensions of a Room
The volume of a room can be represented by the equation x^3 + 10x^2 + 24x, and it's height can be represented by x. What are it's length and width in terms of x?
Dimensions of a Fishtank
The volume of a rectangular fishtank can be represented by the equation x^3 - 4x^2 - 17x + 60, and it's width can be represented by x - 5. What are it's length and height in terms of x?
Cutting Cardboard to Make a Box
A 40cm by 30cm piece of cardboard is used to create a box by cutting a square off of each corner, each with a side length of x. What dimensions of length, width, and height, would produce a box with the greatest volume?
Dimensions of a Bigger Juice Carton
A juice carton has length 4cm, width 3cm, and height 12cm. The manufacturer is designing a new carton with double the volume, by adding a length of x to each dimension. What are the dimensions of the new carton?
Finding a Person's Age
Steve, John, and Peter are all born on February 6. Steve is 5 years older than John, and Peter is 3 years younger than John. In one years, the product of their ages is 11,218 greater than the sum of their ages.