College

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

Answer :

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