High School

The sum of two consecutive odd numbers is 124. What equation would you use 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 find the sum of two consecutive odd numbers that equals 124, let's define how we can represent consecutive odd numbers.

1. Let the first odd number be [tex]\(2x + 1\)[/tex]. Here, [tex]\(x\)[/tex] is an integer, and [tex]\(2x + 1\)[/tex] ensures the number is odd.
2. The next consecutive odd number would be 2 units more than the first odd number. So, it can be represented as [tex]\(2x + 3\)[/tex].

Now, we need to find the sum of these two consecutive odd numbers:
[tex]\[
(2x + 1) + (2x + 3) = 124
\][/tex]

Let's break it down step-by-step:
- The first odd number: [tex]\(2x + 1\)[/tex]
- The second consecutive odd number: [tex]\(2x + 3\)[/tex]
- Their sum: [tex]\((2x + 1) + (2x + 3)\)[/tex]

We can now write the equation representing the sum:
[tex]\[
(2x + 1) + (2x + 3) = 124
\][/tex]

Simplify the left side of the equation:
[tex]\[
2x + 1 + 2x + 3 = 124
\][/tex]
Combine like terms:
[tex]\[
4x + 4 = 124
\][/tex]

Thus, the equation that we would use to solve this problem is:
[tex]\[
\boxed{(2x + 1) + (2x + 3) = 124}
\][/tex]

Looking at the provided options, this matches option (c). So, the correct equation to use is:
\[
\boxed{(2x + 1) + (2x + 3) = 124}
\

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