Question

The length of a rectangular room is 9 less than four times the width, `w`, of the room. What expression represents the area of the room?

Answer 1

OK, we know two things at the outset, but need them translating into algebra.

Explanation:

Firstly, we know the area of a rectangle is length, l x width, w.

Secondly, we are told that the length is 9 units less than 4 times the width, so `l = 4w - 9`. We can substitute this fact into the equation above, to get an expression that only has one unknown, w.

Thus the area,`a = l xx w`
Substitution gives: `a = (4w - 9) xx w`
Expanding the bracket yields: `a = 4w^2 - 9w`