Answer :
To solve this problem, we need to determine the first of two consecutive numbers whose sum is 157. We are given that the equation representing this situation, where [tex]\( n \)[/tex] is the first number, is [tex]\( 2n + 1 = 157 \)[/tex].
Here’s how we can solve it step-by-step:
1. Start with the given equation:
[tex]\[
2n + 1 = 157
\][/tex]
2. Subtract 1 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
This simplifies to:
[tex]\[
2n = 156
\][/tex]
3. Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
This calculation results in:
[tex]\[
n = 78
\][/tex]
Therefore, the first number is 78.
So, the correct answer is:
B. 78
Here’s how we can solve it step-by-step:
1. Start with the given equation:
[tex]\[
2n + 1 = 157
\][/tex]
2. Subtract 1 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
This simplifies to:
[tex]\[
2n = 156
\][/tex]
3. Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
This calculation results in:
[tex]\[
n = 78
\][/tex]
Therefore, the first number is 78.
So, the correct answer is:
B. 78
