Word Problem: A book's page is twice as tall as it is wide.

[snakeyesxlaw]

A page of a book is twice as tall as it is wide. The margins at the top and bottom of the page are 1.5 inches each and the margin on each side is 1 inch.

Write a function that models the area A of the printed portion of the page as a function of the width x of the page.

Width = (2x-3)

Length = (x-2)

A(x) = (x-2)(2x-3)

Suppose the area of the printed matter is 171 square inches. Find the dimensions of the page.

Height =
Width =

** this is where it gets questionable;
** is this correct:

(x-2)(2x-3) = 171
2x^2 - 5x + 6 = 171
2x^2 - 5x + 6 -171 = 0
2x^2 - 5x - 165 = 0

** if using quadratic formula;

(5 + or - (1320) ^ (1/2)) / 4 /* that does not look good at all expecially when solving for x to
/* to plug for the length x width

 

[stapel]

I'm not sure I follow...?

The page is defined in terms of width and height, but you're using "width" and "length" (with "width" in place of "height"?), plus the exercise uses "width" and "height" in terms of the page, but you seem to be referring to the printed area only. I think you mean the following:

. . .page:
. . . . .width: x
. . . . .height: 2x

. . .printed area within page:
. . . . .width: x - 1 - 1 = x - 2
. . . . .height: 2x - 1.5 - 1.5 = 2x - 3

. . .printed-area function:
. . . . .A(x) = (x - 2)(2x - 3)

If so, then I agree with your result. However, you might want to check your multiplication:

. . .(x - 2)(2x - 3)
. . . . .= (x)(2x) + (-2)(2x) + (x)(-3) + (-2)(-3)
. . . . .= 2x² - 4x - 3x + 6
. . . . .= 2x² - 7x + 6

Hope that helps!

Eliz.

 

[Deleted member 4993]

Re: Word Problem: A book's page is twice as tall as it is wi

A page of a book is twice as tall as it is wide. The margins at the top and bottom of the page are 1.5 inches each and the margin on each side is 1 inch.

Write a function that models the area A of the printed portion of the page as a function of the width x of the page.

Width = (2x-3)

Length = (x-2)

A(x) = (x-2)(2x-3)

Suppose the area of the printed matter is 171 square inches. Find the dimensions of the page.

Height =
Width =

** this is where it gets questionable;
** is this correct:

         (x-2)(2x-3) = 171
      2x^2 - 5x + 6 = 171[color=red].............Incorrect It should be

      2x^2 - 7x + 6 = 171[/color]

      2x^2 - 5x + 6 -171 = 0
      2x^2 - 5x - 165 = 0

** if using quadratic formula;

(5 + or - (1320) ^ (1/2))  /  4        /* that does not look good at all expecially when solving for x to
                                                    /* to plug for the length x width[/quote]

 

[snakeyesxlaw]

okay, finally got this together..

the part i messed up on was reading the fine print of 171 being the area of just the printed part where the questions asks for the dimensions of the whole page which would be (2x) and (x) respectively.

so solving for x back at the original equation:

(x-2)(2x-3) = 171
2x^2 - 7x + 6 = 171
2x^2 - 7x -165 = 0
(2x+15)(x-11) = 0
x = 11

so plugging x in for the whole page would be (2x) & (x) is 22 x 11

 

[Deleted member 4993]

okay, finally got this together..

the part i messed up on was reading the fine print of 171 being the area of just the printed part where the questions asks for the dimensions of the whole page which would be (2x) and (x) respectively.

so solving for x back at the original equation:

(x-2)(2x-3) = 171
2x^2 - 7x + 6 = 171
2x^2 - 7x -165 = 0
(2x+15)(x-11) = 0
x = 11

so plugging x in for the whole page would be (2x) & (x) is 22 x 11....Correct....