Answer: We are given that the area of the rectangular room is 750 square feet, and the width of the room is 5 feet less than the length of the room.
Let's use y to represent the length of the room in feet. Then, the width of the room would be y - 5.
The area of a rectangle is given by the product of its length and width. Therefore, we can set up an equation:
y(y - 5) = 750
Expanding the left-hand side, we get:
y^2 - 5y = 750
This is one equation that can be used to solve for y.
Another option is to rearrange the previous equation to get:
y^2 - 5y - 750 = 0
This is a quadratic equation that can be solved using the quadratic formula or factoring.
A third option is to use the equation:
(y + 25)(y - 30) = 0
This equation can be obtained by factoring the previous quadratic equation. The solutions to this equation are y = -25 and y = 30, but since the length of the room cannot be negative, the only valid solution is y = 30.
Therefore, the three equations that can be used to solve for y are:
y(y - 5) = 750
y^2 - 5y - 750 = 0
(y + 25)(y - 30) = 0
Explanation: