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 (1)
Combine like terms: Rewrite the equation n + 5 1 n = 24 as 5 6 n = 24 .
Isolate n : Multiply both sides of the equation by 6 5 to get n = 24 ⋅ 6 5 .
Simplify: Calculate n = 6 24 ⋅ 5 = 6 120 .
Determine the value of n : n = 20 , so the final answer is 20 .
Explanation
Understanding the equation We are given the equation n + f r a c 1 5 n = 24 and asked to solve for n . This equation states that a number n , when added to one-fifth of itself, equals 24.
Combining terms To solve for n , we first combine the terms on the left side of the equation. We can rewrite n as f r a c 5 5 n , so the equation becomes: f r a c 5 5 n + f r a c 1 5 n = 24
Adding fractions Now, we add the fractions: f r a c 6 5 n = 24
Isolating n To isolate n , we multiply both sides of the equation by the reciprocal of f r a c 6 5 , which is f r a c 5 6 :
n = 24 c d o t f r a c 5 6
Simplifying Now, we simplify the expression to find the value of n :
n = f r a c 24 c d o t 5 6 = f r a c 120 6 = 20
Final Answer Therefore, the value of n is 20.
Examples
Imagine you're baking a cake and the recipe calls for a certain amount of flour. However, you decide to add an extra 5 1 of the original amount to make the cake a bit more fluffy. If the final amount of flour you used was 24 cups, this problem helps you determine how much flour the original recipe required. Understanding how to solve such equations is useful in adjusting recipes, managing budgets, or calculating proportions in various real-life situations.
