Sure! Let's take a close look at the number sentence and translate it into an equation step-by-step.
Number sentence: Fourteen more than the quotient of a number and 5 is 23.
1. Identify the unknown quantity:
Let [tex]\( n \)[/tex] be the unknown number we need to find.
2. Understand the parts of the sentence:
- "The quotient of a number and 5" means dividing the number by 5, which can be represented as [tex]\( \frac{n}{5} \)[/tex].
- "Fourteen more than" means we need to add 14 to the result of the quotient.
3. Form the equation:
- Adding 14 to the quotient of [tex]\( n \)[/tex] and 5 gives us [tex]\( \frac{n}{5} + 14 \)[/tex].
- This entire expression is said to "be" 23, which translates into the equation:
[tex]\[
\frac{n}{5} + 14 = 23
\][/tex]
So, the equation that represents the given number sentence is:
[tex]\[
\frac{n}{5} + 14 = 23
\][/tex]
Examining the choices provided:
[tex]\[
\begin{array}{l}
\frac{n+14}{5}=23 \\
\frac{5}{n+14}=23 \\
\frac{5}{n}+14=23 \\
\frac{n}{5}+14=23
\end{array}
\][/tex]
Only the fourth equation matches our derived equation.
Thus, the correct answer is:
[tex]\[
\frac{n}{5} + 14 = 23
\][/tex]
This corresponds to the fourth option.
