College

Select the correct answer.

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

What is the first number?

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

Answer :

To find the first number, we need to understand the given situation: the sum of two consecutive numbers is 157. We are given the equation where [tex]\( n \)[/tex] is the first number:

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

This equation represents the sum of the first number ([tex]\( n \)[/tex]) and the next consecutive number ([tex]\( n + 1 \)[/tex]), expressed as:

- First number: [tex]\( n \)[/tex]
- Second number: [tex]\( n + 1 \)[/tex]

So, their sum is:

[tex]\[ n + (n + 1) = 2n + 1 \][/tex]

Now, let's solve the equation [tex]\( 2n + 1 = 157 \)[/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]

Therefore, the first number is 78. The correct answer is:

B. 78