Explanation:
The area of a rectangular room is given by the formula A = l * w, where l is the length and w is the width. In this case, we know that A = 750 square feet and w = l - 5 feet. We can use this information to create equations to solve for the length of the room.
Three options that can be used to solve for y are:
y(y + 5) = 750
This equation can be obtained by substituting the given information into the formula for the area of a rectangular room.
y(l - 5) = 750
y(l) - 5y = 750
y2 – 5y = 750
This equation can be obtained by expanding the first equation and moving all the terms to one side of the equation.
y(l) - 5y = 750
y2 - 5y = 750
(y + 25)(y - 30) = 0
This equation can be obtained by factoring the second equation, in which you get two solutions, y = -25 and y = 30. The first solution is not a valid solution because the length of a room can not be negative but the second one is a valid solution.
Note that 750 - y(y - 5) = 0 and y(y - 5) + 750 = 0 are not valid options as they are not equation that can be used to solve for y.