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Answer :
To find the first of the two consecutive numbers whose sum is 157, we start by considering the equation [tex]\(2n + 1 = 157\)[/tex]. Here, [tex]\(n\)[/tex] represents the first number, and [tex]\(n + 1\)[/tex] represents the second number, because consecutive numbers differ by 1.
Let's go through the steps to solve for [tex]\(n\)[/tex]:
1. Set up the equation:
[tex]\[
2n + 1 = 157
\][/tex]
2. Subtract 1 from both sides to eliminate the constant term on the left side:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
3. Divide both sides by 2 to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
[tex]\[
n = 78
\][/tex]
Thus, the first number is [tex]\(\boxed{78}\)[/tex], which matches option B.
Let's go through the steps to solve for [tex]\(n\)[/tex]:
1. Set up the equation:
[tex]\[
2n + 1 = 157
\][/tex]
2. Subtract 1 from both sides to eliminate the constant term on the left side:
[tex]\[
2n + 1 - 1 = 157 - 1
\][/tex]
[tex]\[
2n = 156
\][/tex]
3. Divide both sides by 2 to solve for [tex]\(n\)[/tex]:
[tex]\[
n = \frac{156}{2}
\][/tex]
[tex]\[
n = 78
\][/tex]
Thus, the first number is [tex]\(\boxed{78}\)[/tex], which matches option B.
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