High School

The sum of two consecutive odd numbers is 124. What equation should be used to solve this problem?

A. [tex]2x + 1 = 124[/tex]
B. [tex]2x + x = 124[/tex]
C. [tex](2x + 1) + (2x + 3) = 124[/tex]
D. [tex]x + (x + 1) = 124[/tex]

Answer :

To solve the problem of finding two consecutive odd numbers whose sum is 124, we need to set up an equation.

1. Define the consecutive odd numbers:
Let’s represent the first odd number as [tex]\(2x + 1\)[/tex]. Consecutive odd numbers differ by 2, so the next odd number would be [tex]\(2x + 3\)[/tex].

2. Set up the equation:
The problem states that the sum of these two consecutive odd numbers is 124. Therefore, we can write the equation as:
[tex]\[
(2x + 1) + (2x + 3) = 124
\][/tex]

3. Select the correct choice from the given options:
The equation we formed matches choice c: [tex]\((2x + 1) + (2x + 3) = 124\)[/tex].

So, the equation to use for solving this problem is [tex]\((2x + 1) + (2x + 3) = 124\)[/tex], and the correct choice is c.