College

The sum of two consecutive numbers is 157. This equation, where [tex]n[/tex] is the first number, represents the situation: [tex]2n + 1 = 157[/tex].

What is the first number?

A. 77
B. 78
C. 79
D. 80

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.