Chapter 9.6, Problem 49PPS

(a)

To determine

Solve the area.

Answer to Problem 49PPS

  $375i{n}^2$

Explanation of Solution

Given Information: Width of poster = 25 in. and Length of poster = 20 in

Formula Used: Area of entire poster = $Length\times Width$

Calculation:

Length of poster = 20 in.

Width of poster = 25 in.

Length of area covered by text = $20-\left(x+x\right)=20-2x$

Width of area covered by text = $25-\left(4x+3x\right)=25-7x$

Area of entire poster = $Length\times Width$

So,

Area of entire poster = $20\times 25$

Hence,

Area of entire poster = $500i{n}^2$

As Bartolo wants area with text to be three-fourths of total area $500\times \frac{3}{4}=375i{n}^2$

(b)

To determine

Solve the area.

Answer to Problem 49PPS

  $x=12.9$ or $x=0.7$

Explanation of Solution

Given Information: Area of text = $375i{n}^2$ , Width of poster covered with text = $25-7x$ in. and Length of poster covered with text= $20-2x$ in

Formula Used: $D=b^2-4ac$

Calculation:

• $D$ equal to negative so $x$ has no real solution.
• $D$ equal to 0 so $x$ has 1 real solution.
• $D$ equal to positive so $x$ has 2 real solution.

Length of area covered by text = $20-\left(x+x\right)=20-2x$

Width of area covered by text = $25-\left(4x+3x\right)=25-7x$

  $\left(20-2x\right)\left(25-7x\right)=375$

Now,

  $14x^2-190x+125=0$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=14,b=-190$ and $c=125$

  $D={\left(-190\right)}^2-4\times 14\times 125$

Now,

  $D=36100-7000$

Hence,

  $D=29100$

As, $D$ equal to positive so $x$ has 2 real solution

  $x=\frac{-b\pm \sqrt{D}}{2a}$

So,

  $x=\frac{-\left(-190\right)\pm \sqrt{29100}}{2\times 14}$

Now, square root of 29100 is 170.6

  $x=\frac{190\pm 170.6}{28}$

Now,

  $x=\frac{190+170.6}{28}$ or $x=\frac{190-170.6}{28}$

Now,

  $x=\frac{360.6}{28}$ or $x=\frac{19.4}{28}$

Now,

  $x=12.9$ or $x=0.7$

(c)

To determine

Solve the equation.

Answer to Problem 49PPS

Sides = $0.7$ in.

Top = $2.8$ in.

Bottom = $2.1$ in.

Explanation of Solution

Given Information: Margin $x=0.7$

Calculation:

Margins on the sides = $x=0.7$ in.

Margins on the top = $4x=4\times 0.7=2.8$ in.

Margins on the bottom = $3x=3\times 0.7=2.1$ in.