High School

Select the correct answer.

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 :

Let's solve the problem step-by-step!

We know that we have two consecutive numbers whose sum is 157. Let's represent the first number as [tex]\( n \)[/tex]. Since the numbers are consecutive, the second number will be [tex]\( n + 1 \)[/tex].

The problem tells us that their sum is 157, so we can write the equation:

[tex]\[ n + (n + 1) = 157 \][/tex]

Simplify the equation:

[tex]\[ 2n + 1 = 157 \][/tex]

Now, we need to solve for [tex]\( n \)[/tex]. We'll start by isolating [tex]\( n \)[/tex] on one side of the equation.

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]

Therefore, the first number is 78.

So, the correct answer is:

B. 78