(1) A number, [tex]$n$[/tex], is added to 16 less than 3 times itself. The result is 101. Which equation can be used to find [tex]$n$[/tex]?
A. [tex]$3 n-16+n=101$[/tex]
B. [tex]$3 n+16+n=101$[/tex]
C. [tex]$3 n-16-n=101$[/tex]
D. [tex]$3 n+16-n=101$[/tex]
Answer (1)
Translate '16 less than 3 times itself' to 3 n − 16 .
Add the number n to the expression: 3 n − 16 + n .
Set the result equal to 101: 3 n − 16 + n = 101 .
The correct equation is 3 n − 16 + 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 the phrase "16 less than 3 times itself" into an algebraic expression. "3 times itself" refers to 3 n , and "16 less than" means we subtract 16 from that. So, the expression is 3 n − 16 .
Adding the Number n Next, the problem states that the number n is added to this expression. So we add n to 3 n − 16 , which gives us 3 n − 16 + n .
Forming the Equation Finally, we are told that the result of this addition is 101. Therefore, we set our expression equal to 101: 3 n − 16 + n = 101 .
Identifying the Correct Equation Comparing our equation 3 n − 16 + n = 101 with the given options, we see that it matches the first option.
Final Answer Therefore, the equation that can be used to find the value of n is 3 n − 16 + n = 101 .
Examples
Imagine you're saving up for a new video game that costs $101. You already have some money, but you need to triple it and then subtract $16 for a special discount. If you add the original amount you had to the discounted triple amount, you'll have exactly $101. The equation 3 n − 16 + n = 101 helps you figure out how much money you started with.
