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 :

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.