Question

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.

Which equations can be used to solve for y, the length of the room? Select three options.

y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0

Answer 1

Correct choices: 2, 3, and 5.

Reason: width = y − 5, area gives y(y − 5) = 750. That is equivalent to
- y^2 − 5y = 750 (option 2),
- 750 − y(y − 5) = 0 (option 3),
and rearranged y^2 − 5y − 750 = 0 factors as (y + 25)(y − 30) = 0 (option 5).

(Reject options 1 and 4 because they give incorrect signs.)