A number, $n$, is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of $n$?
$3 n-15+n=101$
$3 n+15+n=101$
$3 n-15-n=101$
$3 n+15-n=101$
Answer (1)
Translate '15 less than 3 times itself' to 3 n − 15 .
Add n to the expression: 3 n − 15 + n .
Set the result equal to 101: 3 n − 15 + n = 101 .
The equation to find the value of n is 3 n − 15 + n = 101 .
\boxed{3 n-15+n=101}
Explanation
Understanding the Problem Let's break down the problem step by step to form the correct equation.
Translating the Words into Algebra The problem states that a number, n , is added to '15 less than 3 times itself'. '3 times itself' can be written as 3 n . '15 less than 3 times itself' can be written as 3 n − 15 .
Forming the Expression We are told that n is added to 3 n − 15 . This gives us the expression 3 n − 15 + n .
Writing the Equation The problem states that the result of this addition is 101. Therefore, we can write the equation as 3 n − 15 + n = 101 .
Final Answer Therefore, the correct equation is 3 n − 15 + n = 101 .
Examples
Imagine you're trying to figure out how many apples you have. You know that if you take 15 apples away from three times the number of apples you have, and then add the original number of apples back, you end up with 101 apples. This equation helps you find out how many apples you started with. This kind of problem is useful in inventory management, where you need to track stock levels after additions and subtractions. It's also applicable in budgeting, where you might calculate expenses and income to reach a final balance.
