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]
