Select the correct answer.
The sum of two consecutive numbers is 157. This equation, where [tex]$n$[/tex] is the first number, represents the situation: [tex]$2n + 1 = 157$[/tex].
What is the first number?
A. 77
B. 78
C. 79
D. 80
Answer (2)
Start with the equation 2 n + 1 = 157 .
Subtract 1 from both sides: 2 n = 156 .
Divide both sides by 2: n = 78 .
The first number is 78 .
Explanation
Understanding the Problem We are given that the sum of two consecutive numbers is 157, and the equation representing this situation is 2 n + 1 = 157 , where n is the first number. Our goal is to find the value of n .
Isolating the Term with n To solve for n , we need to isolate n on one side of the equation. First, we subtract 1 from both sides of the equation: 2 n + 1 − 1 = 157 − 1 2 n = 156
Solving for n Next, we divide both sides of the equation by 2 to solve for n :
2 2 n = 2 156 n = 78
Finding the First Number Therefore, the first number is 78.
Examples
Consider a scenario where you and a friend are collecting seashells on a beach. You know that together, you've collected 157 seashells, and you've collected one more shell than your friend. Using the equation 2 n + 1 = 157 , where n represents the number of seashells your friend collected, you can determine that your friend collected 78 seashells, and you collected 79. This problem demonstrates how algebraic equations can be used to solve everyday counting problems.
The first of the two consecutive numbers is 78, as derived from the equation 2 n + 1 = 157 . After isolating n and solving, we find that n = 78 . Therefore, the correct answer is option B: 78.
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