Question

Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five less than half its width. Complete the equation that can be used to determine the dimensions of the monitor in terms of its width, w.

(Blank) x^2 + (Blank) x = (Blank)

Answer 1

`3w^2 - 30w=384`

Explanation:

Let's say the length is l and the width is w. Since the problem says that the length is "six times the quantity of five less than half its width", we can write the equation:

l = 6 * (w/2 - 5)

Now, the area of a rectangle is of the form: A = lw, where l is the length and w is the width. We can substitute the expression of l above into the equation:

`(6*(w/2 - 5))*w=384`

`(3w - 30)*w=384`

`3w^2 - 30w=384`

Hope this helps!

Answer 2

Let w equal the width.

The length of the monitor is six times the quantity of five less than half its width can be written as [ 6(w/2-5) ]

Simplify that expression.

= 6(w/2-5)

= 3w - 30

The area can be find by using [ A = bh ]

Substitute with the given values.

w * (3w - 30) = 384

3w² - 30w = 384

Therefore, the answer is 3w² - 30w = 384

Best of Luck!