Chapter 4.5, Problem 45HP

(a)

To determine

To calculate:Tomake a function table to show the amount of fencing needed for widths $12,15$ and $18$ feet

Answer to Problem 45HP

Function table is

Width (in feet)	12	15	18
Fencing Needed (in feet)	48	50	60

Explanation of Solution

Given information:Equation that represents the relationship between the width of fenced area and the total amount of fencing needed is $2w+24=f$

Calculation:

Equation that represents the relationship between the width of fenced area and the total amount of fencing needed is given as follows

  $2w+24=f$

When $w=12$ , amount of fencing needed, $f=2\left(12\right)+24=24+24=48$ feet

When $w=15$ , amount of fencing needed, $f=2\left(15\right)+24=30+24=54$ feet

When $w=18$ , amount of fencing needed, $f=2\left(18\right)+24=36+24=60$ feet

Function table is as follows:

Width (in feet)	12	15	18
Fencing Needed (in feet)	48	50	60

(b)

To determine

To calculate: Tofind the width of the fenced area if Tia has $92$ feet of fencing

Answer to Problem 45HP

Width of fenced area is $34$ feet.

Explanation of Solution

Given information:Equation that represents the relationship between the width of fenced area and the total amount of fencing needed is $2w+24=f$

Calculation:

Equation that represents the relationship between the width of fenced area and the total amount of fencing needed is given as follows

  $2w+24=f$

Total fencing $=92$ feet

Thus, width of fenced area is calculated as follows:

  $2x+24=92$

On solving the above,

  $\begin{array}{l}2x=92-24\\ 2x=68\\ x=\frac{68}{2}\\ x=34\end{array}$

Hence, width of fenced area is $34$ feet.