Answer :
Sure! Let's solve the problem step-by-step.
We are given that the sum of two consecutive numbers is 157. If we represent the first number as [tex]\( n \)[/tex], then the next consecutive number would be [tex]\( n + 1 \)[/tex].
The equation describing this situation is:
[tex]\[ n + (n + 1) = 157 \][/tex]
Simplify this equation:
[tex]\[ n + n + 1 = 157 \][/tex]
Combine like terms:
[tex]\[ 2n + 1 = 157 \][/tex]
Now we need to solve the equation [tex]\( 2n + 1 = 157 \)[/tex] to find the value of [tex]\( n \)[/tex].
1. Subtract 1 from both sides of the equation:
[tex]\[ 2n = 157 - 1 \][/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]
So, the first number is [tex]\( n = 78 \)[/tex]. Therefore, the correct answer is B. 78.
We are given that the sum of two consecutive numbers is 157. If we represent the first number as [tex]\( n \)[/tex], then the next consecutive number would be [tex]\( n + 1 \)[/tex].
The equation describing this situation is:
[tex]\[ n + (n + 1) = 157 \][/tex]
Simplify this equation:
[tex]\[ n + n + 1 = 157 \][/tex]
Combine like terms:
[tex]\[ 2n + 1 = 157 \][/tex]
Now we need to solve the equation [tex]\( 2n + 1 = 157 \)[/tex] to find the value of [tex]\( n \)[/tex].
1. Subtract 1 from both sides of the equation:
[tex]\[ 2n = 157 - 1 \][/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]
So, the first number is [tex]\( n = 78 \)[/tex]. Therefore, the correct answer is B. 78.
