Select the correct answer.
The sum of two consecutive numbers is 157. This equation, where $n$ is the first number, represents the situation: $2n+1=157$
What is the first number?
A. 77
B. 78
C. 79
D. 80
Answer (2)
Subtract 1 from both sides of the equation: 2 n + 1 = 157 becomes 2 n = 156 .
Divide both sides by 2: 2 n = 156 becomes n = 2 156 .
Calculate the value of n : 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 variable 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
Simplifying the equation This simplifies to: 2 n = 156
Solving for n Next, we divide both sides of the equation by 2: n = 2 156
Calculating the result Calculating the value of n , we get: n = 78
Final Answer 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 also know that your friend collected one more shell than you did. Using the equation 2 n + 1 = 157 , you can determine that you collected 78 seashells, and your friend collected 79. This problem demonstrates how algebraic equations can be used to solve real-world problems involving consecutive numbers and sums.
The first number is 78, which is found by solving the equation 2 n + 1 = 157 . By isolating n , we determine that n = 78 . The second consecutive number is 79, confirming the sum is 157.
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