Get the most out of your questions with the extensive resources available on IDNLearn.com. Join our knowledgeable community to find the answers you need for any topic or issue.

The quotient of a number, [tex]$z$[/tex], and 21 is 42.

Which equation and value of [tex]$z$[/tex] represent this relationship?

A. [tex]\frac{z}{21} = 42 \Rightarrow z = 882[/tex]
B. [tex]21z = 42 \Rightarrow z = 2[/tex]
C. [tex]\frac{1}{21}z = 42 \Rightarrow z = 882[/tex]


Sagot :

Let's break down the problem step by step.

The problem states that the quotient of a number [tex]\( z \)[/tex] and 21 is 42. We can translate this relationship into a mathematical equation.

### Step-by-Step Explanation:

1. Understanding the Quotient:
- The quotient of a number [tex]\( z \)[/tex] and 21 means [tex]\( \frac{z}{21} \)[/tex].

2. Setting Up the Equation:
- According to the problem, [tex]\( \frac{z}{21} = 42 \)[/tex].

3. Solving for [tex]\( z \)[/tex]:
- To find the value of [tex]\( z \)[/tex], multiply both sides of the equation by 21 (to get rid of the fraction):
[tex]\[ \frac{z}{21} \cdot 21 = 42 \cdot 21 \][/tex]
- Simplifying the left-hand side:
[tex]\[ z = 42 \cdot 21 \][/tex]

4. Calculating the Value:
- Now we calculate:
[tex]\[ z = 42 \cdot 21 = 882 \][/tex]

Therefore, the equation representing the relationship is [tex]\( \frac{z}{21} = 42 \)[/tex], and solving this gives [tex]\( z = 882 \)[/tex].

So the appropriate equation and value of [tex]\( z \)[/tex] are shown as:
[tex]\[ 21z = 42 \quad \rightarrow \quad z = 882 \][/tex]