Chapter 8.4, Problem 7CYU

(a)

To determine

The equation to model this situation.

Answer to Problem 7CYU

  $\frac{x}{4}=\frac{9}{x}$

Explanation of Solution

Given:

The ratio of an integer to 4 is the same as the ratio of 9 to that integer.

Concept Used:

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:

Let the integer be x . Then, as per the statement the ratio of x to 4 is the same as the ratio of 9 to x .

Thus, the equation to model this situation is $\frac{x}{4}=\frac{9}{x}$ .

(b)

To determine

The possible value of x .

Answer to Problem 7CYU

  $x=-6,6$

Explanation of Solution

Given:

The ratio of an integer to 4 is the same as the ratio of 9 to that integer.

Concept Used:

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 possible values of x is $\frac{x}{4}=\frac{9}{x}$ , and simplify further as shown below:

  $\begin{array}{c}\frac{x}{4}=\frac{9}{x}\\ \frac{x}{4}\cdot x=\frac{9}{x}\cdot x\\ \frac{x^2}{4}=9\\ \frac{x^2}{4\cdot 9}=\frac{9}{9}\\ \frac{x^2}{36}=1\\ \frac{x^2}{36}\cdot 36=36\\ x^2=36\\ x=\pm \sqrt{36}\\ x=+6\text{and}-6\end{array}$

Thus, the possible values of x is $x=+6\text{and}-6$ .