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 of $n$?
Answer (2)
The value of n is 20 .
Explanation
Understanding the Problem We are given the equation n + 5 1 n = 24 and we want to find the value of n . This equation represents a number n added to one-fifth of itself, which equals 24.
Combining Like Terms To solve for n , we first combine the terms on the left side of the equation. We can rewrite n as 5 5 n , so the equation becomes: 5 5 n + 5 1 n = 24
Adding Fractions Now, we add the fractions: 5 5 + 1 n = 24
5 6 n = 24
Isolating n To isolate n , we multiply both sides of the equation by the reciprocal of 5 6 , which is 6 5 :
6 5 ⋅ 5 6 n = 24 ⋅ 6 5
Simplifying Now, we simplify: n = 6 24 ⋅ 5 n = 6 120 n = 20
Final Answer Therefore, the value of n is 20.
Examples
Imagine you're saving money, and you decide to add one-fifth of your current savings to your savings account. If the total amount in your account after this addition is $24, this problem helps you calculate how much money you initially had in your savings account. Understanding how to solve such equations can help you manage your finances and understand proportional increases in real-life scenarios.
The value of n is 20, as it combines with one-fifth of itself to equal 24. This was found by rearranging and simplifying the equation n + 5 1 n = 24 .
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