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

y^2 - 5y = 750

Explanation:

If length = y

then width = y - 5

Area = length x width

= y(y-5) = 750

Or, y^2 - 5y = 750

This equation can be further solved as follows:

y^2 - 5y - 750 = 0

Or, y^2 - 30y + 25y - 750 = 0

Or, y(y - 30) + 25(y - 30) = 0

Or, (y + 25)(y-30) = 0

So, there are two possibilities:

If (y + 25) = 0

then y = -25

but value of length cannot be negative,

Let us look at second possibility

If (y - 30) = 0

then y = 30

So, length = 30 feet

Check Answer:

Length = 30 feet

so, width = 30 - 5 = 25 feet

so, area = 30 x 25 = 750 square feet