High School

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 :

To find the first number in the sequence of two consecutive numbers whose sum is 157, you can follow these steps:

1. Understand the problem: You have two consecutive numbers. If the first number is [tex]\( n \)[/tex], the next consecutive number would be [tex]\( n + 1 \)[/tex].

2. Set up the equation: According to the problem, these two numbers add up to 157. Therefore, the equation is:
[tex]\[
n + (n + 1) = 157
\][/tex]

3. Simplify the equation: Combine the terms with [tex]\( n \)[/tex].
[tex]\[
n + n + 1 = 157
\][/tex]

This simplifies to:
[tex]\[
2n + 1 = 157
\][/tex]

4. Solve for [tex]\( n \)[/tex]:
- Subtract 1 from both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n = 157 - 1
\][/tex]

- Simplify the right side:
[tex]\[
2n = 156
\][/tex]

- Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]

- Calculate the value:
[tex]\[
n = 78
\][/tex]

So, the first number is 78. Therefore, the correct answer is B. 78.