Question

when a number is added to \\(\frac{1}{5}\\) of itself, the result is 24. the equation that models this problem is \\(n + \frac{1}{5}n = 24\\).

what is the value \\(n\\)?

\\(n = 18\\)
\\(n = 20\\)
\\(n = 21\frac{4}{5}\\)
\\(n = 23\frac{4}{5}\\)

Explanation:

Identify the given equation

We are given the linear equation that models the word problem:

$$ n + \frac{1}{5}n = 24 $$

Our goal is to solve this equation for the unknown variable \(n\).

Combine the like terms

To combine the terms on the left side, we find a common denominator for the coefficients of \(n\). The coefficient of the first term is \(1\), which can be written as \(\frac{5}{5}\):

$$ \frac{5}{5}n + \frac{1}{5}n = 24 $$

Adding the fractions gives:

$$ \frac{6}{5}n = 24 $$

Isolate the variable n

To solve for \(n\), we multiply both sides of the equation by the reciprocal of \(\frac{6}{5}\), which is \(\frac{5}{6}\):

$$ n = 24 \times \frac{5}{6} $$

Simplify the expression

We simplify the multiplication by dividing \(24\) by \(6\) first:

$$ n = 4 \times 5 $$

$$ n = 20 $$

This matches the second option.

Answer:

• (A) \(n = 18\)
• (B) \(n = 20\) (Correct answer)
• (C) \(n = 21\frac{4}{5}\)
• (D) \(n = 23\frac{4}{5}\)