Answer :
Sure! Let's solve the problem step-by-step.
We are given that the sum of two consecutive numbers is 157, and we need to represent this situation using an equation where `n` is the first number.
Since the numbers are consecutive, if the first number is `n`, the second number would be `n + 1`.
According to the problem, the sum of these two numbers is 157. So, we can write the equation as:
[tex]\[ n + (n + 1) = 157 \][/tex]
Simplify the equation:
[tex]\[ n + n + 1 = 157 \][/tex]
Combine like terms:
[tex]\[ 2n + 1 = 157 \][/tex]
Now, we need to solve for `n`.
First, subtract 1 from both sides:
[tex]\[ 2n = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
Next, divide both sides by 2:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
So, the first number is [tex]\( \boxed{78} \)[/tex].
Therefore, the correct answer is B. 78.
We are given that the sum of two consecutive numbers is 157, and we need to represent this situation using an equation where `n` is the first number.
Since the numbers are consecutive, if the first number is `n`, the second number would be `n + 1`.
According to the problem, the sum of these two numbers is 157. So, we can write the equation as:
[tex]\[ n + (n + 1) = 157 \][/tex]
Simplify the equation:
[tex]\[ n + n + 1 = 157 \][/tex]
Combine like terms:
[tex]\[ 2n + 1 = 157 \][/tex]
Now, we need to solve for `n`.
First, subtract 1 from both sides:
[tex]\[ 2n = 157 - 1 \][/tex]
[tex]\[ 2n = 156 \][/tex]
Next, divide both sides by 2:
[tex]\[ n = \frac{156}{2} \][/tex]
[tex]\[ n = 78 \][/tex]
So, the first number is [tex]\( \boxed{78} \)[/tex].
Therefore, the correct answer is B. 78.
