Chapter 8.2, Problem 68IP

(a)

To determine

Make a function table to show the amount of fencing needed for width of $12,15\text{and}18\text{feet}$

Answer to Problem 68IP

The table is below

Width w	12	15	18
Fencing $2w+24=f$	48	54	60

Explanation of Solution

Given:

Tia’s family is installing a fence around three sides of her backyard as shown below

  

The equations, $2w+24=f$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to make a table for widths $12,15\text{and}18\text{feet}$ by the help of the equation is below:

  $\begin{array}{l}2w+24=f\\ w=12\\ 2\cdot 12+24=f\\ 24+24=f\\ 48=f\\ \Rightarrow f=48\\ w=15\\ 2\cdot 15+24=f\\ 54=f\\ \Rightarrow f=54\\ w=18\\ 2\cdot 18+24=f\\ 60=f\\ \Rightarrow f=60\end{array}$

Thus, the table is below

Width w	12	15	18
Fencing $2w+24=f$	48	54	60

(b)

To determine

The width of the fenced area if Tia has 92 feet of fencing

Answer to Problem 68IP

The width of fenced area is $w=34$ .

Explanation of Solution

Given:

The equation, $2w+24=f$ and $f=92$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the width of the fenced area if Tia has 92 feet of fencing as shown below,

  $\begin{array}{c}2w+24=f\\ f=92\\ 2w+24=92\\ 2w+24-24=92-24\\ 2w=68\\ \frac{2w}{2}=\frac{68}{2}\\ w=34\end{array}$

Thus, the width of fenced area is $w=34$ .