College

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 [tex]$n$[/tex] be the first number. The sum of two consecutive numbers is given by

[tex]$$
n + (n+1) = 2n + 1.
$$[/tex]

We know that the sum is 157, so we set up the equation

[tex]$$
2n + 1 = 157.
$$[/tex]

Subtract 1 from both sides to isolate the term with [tex]$n$[/tex]:

[tex]$$
2n = 157 - 1 = 156.
$$[/tex]

Now, divide both sides by 2 to solve for [tex]$n$[/tex]:

[tex]$$
n = \frac{156}{2} = 78.
$$[/tex]

Thus, the first number is [tex]$78$[/tex], which corresponds to answer choice B.

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