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 $n$?
A. $3n-15+n=101$
B. $3n+15+n=101$
C. $3n-15-n=101$
D. $3n+15-n=101
Answer (1)
Translate '15 less than 3 times itself' to 3 n − 15 .
Add the number n to the expression: ( 3 n − 15 ) + n .
Set the result equal to 101: 3 n − 15 + n = 101 .
The correct equation is 3 n − 15 + n = 101 .
Explanation
Problem Analysis Let's break down the problem step by step to form the correct equation.
Translating the Phrase First, we need to translate "15 less than 3 times itself" into an algebraic expression. "3 times itself" means 3 n , and "15 less than" means we subtract 15 from that. So, the expression is 3 n − 15 .
Adding the Number n Next, we add the number n to this expression. So we have ( 3 n − 15 ) + n .
Forming the Equation Finally, we know that the result of this addition is 101. Therefore, the equation is 3 n − 15 + n = 101 .
Identifying the Correct Equation Comparing this equation with the given options, we see that it matches the first option: 3 n − 15 + n = 101 .
Final Answer Therefore, the correct equation is 3 n − 15 + n = 101 .
Examples
Imagine you are trying to figure out how many apples you have. You know that if you triple the number of apples you have and then give away 15, and then add the original number of apples back, you would have 101 apples. This equation helps you determine the original number of apples you started with. This kind of problem helps in inventory management, budgeting, and resource allocation.
