Answer :
To solve the problem of finding the first number of two consecutive numbers that add up to 157, let's break it down step by step based on the equation provided:
1. Understand the equation:
We are given that the sum of two consecutive numbers is 157. If we let the first number be [tex]\( n \)[/tex], the consecutive number would be [tex]\( n + 1 \)[/tex]. So, the equation representing this situation is:
[tex]\[
n + (n + 1) = 157
\][/tex]
2. Simplify the equation:
Combine the like terms (the [tex]\( n \)[/tex] terms):
[tex]\[
n + n + 1 = 157 \\
2n + 1 = 157
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
First, subtract 1 from both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n = 157 - 1 \\
2n = 156
\][/tex]
Next, divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2} \\
n = 78
\][/tex]
So, the first number is 78, which corresponds to option B.
1. Understand the equation:
We are given that the sum of two consecutive numbers is 157. If we let the first number be [tex]\( n \)[/tex], the consecutive number would be [tex]\( n + 1 \)[/tex]. So, the equation representing this situation is:
[tex]\[
n + (n + 1) = 157
\][/tex]
2. Simplify the equation:
Combine the like terms (the [tex]\( n \)[/tex] terms):
[tex]\[
n + n + 1 = 157 \\
2n + 1 = 157
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
First, subtract 1 from both sides of the equation to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n = 157 - 1 \\
2n = 156
\][/tex]
Next, divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{156}{2} \\
n = 78
\][/tex]
So, the first number is 78, which corresponds to option B.
