Question

The area of the conference table in Mr. Nathan’s office must be no more that 175 ft^2. If the length of the table is 18 ft more that the width, x, which interval can be the possible widths ?

Answer 1

(0, 7]

Explanation:

Let's call the width W and the length L. The length is 18 feet more than the width, so:

L = W + 18

The area can be no more than 175, so:

A ≤ 175

LW ≤ 175

Since L = W + 18:

(W + 18) W ≤ 175

W² + 18W ≤ 175

W² + 18W - 175 ≤ 0

(W - 7) (W + 25) ≤ 0

-25 ≤ W ≤ 7

However, the width of the table can't be nonpositive, so:

0 < W ≤ 7

Or in interval notation, (0, 7].