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------------------------------------------------ Select the correct answer.

The sum of two consecutive numbers is 157. This equation is [tex]2n + 1 = 157[/tex].

What is the first number?

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

To solve the problem of finding the first number in two consecutive numbers that sum up to 157, we can use the given equation:

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

Here’s a step-by-step solution:

1. Understand the equation: The equation [tex]\(2n + 1 = 157\)[/tex] describes the sum of two consecutive numbers. The first number is [tex]\(n\)[/tex], and since the numbers are consecutive, the second number is [tex]\(n + 1\)[/tex]. Therefore, the equation becomes:

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

Simplifying this gives us the equivalent equation:

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

2. Isolate the variable [tex]\(n\)[/tex]: We want to solve for [tex]\(n\)[/tex]. Begin by subtracting 1 from both sides to isolate the term with [tex]\(n\)[/tex]:

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

[tex]\[ 2n = 156 \][/tex]

3. Solve for [tex]\(n\)[/tex]: Now, divide both sides by 2 to solve for [tex]\(n\)[/tex]:

[tex]\[ n = \frac{156}{2} \][/tex]

[tex]\[ n = 78 \][/tex]

Thus, the first number is [tex]\(78\)[/tex].

So the correct answer is:

B. 78