Answer :
To solve the problem of finding the first number when the sum of two consecutive numbers is 157, let's define the scenario:
Let [tex]\( n \)[/tex] be the first number. The next consecutive number will then be [tex]\( n + 1 \)[/tex].
The equation that represents the sum of these two consecutive numbers is:
[tex]\[ n + (n + 1) = 157 \][/tex]
Now, simplify the equation:
1. Combine like terms:
[tex]\[ 2n + 1 = 157 \][/tex]
2. To find [tex]\( n \)[/tex], first subtract 1 from both sides of the equation:
[tex]\[ 2n = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
3. Divide both sides of the equation by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
Therefore, the first number is [tex]\(\boxed{78}\)[/tex], which corresponds to option B.
Let [tex]\( n \)[/tex] be the first number. The next consecutive number will then be [tex]\( n + 1 \)[/tex].
The equation that represents the sum of these two consecutive numbers is:
[tex]\[ n + (n + 1) = 157 \][/tex]
Now, simplify the equation:
1. Combine like terms:
[tex]\[ 2n + 1 = 157 \][/tex]
2. To find [tex]\( n \)[/tex], first subtract 1 from both sides of the equation:
[tex]\[ 2n = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
3. Divide both sides of the equation by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
Therefore, the first number is [tex]\(\boxed{78}\)[/tex], which corresponds to option B.
