Answer :
To find the first number in the sum of two consecutive numbers that equals 157, we start with the equation given in the problem:
[tex]\[ 2n + 1 = 157 \][/tex]
Here, [tex]\( n \)[/tex] represents the first number, and the next consecutive number is [tex]\( n + 1 \)[/tex]. Let's solve the equation step by step:
1. Subtract 1 from both sides:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
2. Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
[tex]\[
n = 78
\][/tex]
Therefore, the first number is 78. So, the correct answer is:
B. 78
[tex]\[ 2n + 1 = 157 \][/tex]
Here, [tex]\( n \)[/tex] represents the first number, and the next consecutive number is [tex]\( n + 1 \)[/tex]. Let's solve the equation step by step:
1. Subtract 1 from both sides:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
2. Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
[tex]\[
n = 78
\][/tex]
Therefore, the first number is 78. So, the correct answer is:
B. 78