Ethan sells red and blue balloons. Yesterday, he sold a total of 186 balloons, where 62 of them were red. The variable [tex]$p$[/tex] represents the number of blue balloons.

Determine whether each equation correctly represents the number of blue balloons Ethan sold. Select True or False for each equation.

A. [tex]$62p = 186$[/tex]

B. [tex]$62 + p = 186$[/tex]

C. [tex]$186 + p = 62$[/tex]

Let's determine whether each equation correctly represents the number of blue balloons Ethan sold:

1. Understanding the Problem:
- Ethan sold a total of 186 balloons.
- Out of these, 62 were red balloons.
- We need to find the value of blue balloons, represented by [tex]$ p $[/tex].

2. Calculating Blue Balloons:
- To find the number of blue balloons, subtract the red balloons from the total balloons:
[tex]\[
p = 186 - 62 = 124
\][/tex]
- So, Ethan sold 124 blue balloons.

3. Evaluating the Equations:

- Equation 1: [tex]$ 62p = 186 $[/tex]
- This equation suggests multiplying the number of red balloons by the number of blue balloons equals the total balloons, which isn't right. Thus, this equation is False.

- Equation 2: [tex]$ 62 + p = 186 $[/tex]
- This equation is correct because it shows that adding the number of red balloons to the number of blue balloons totals the same number of balloons sold. Thus, this equation is True.

- Equation 3: [tex]$ 186 + p = 62 $[/tex]
- This equation suggests adding the total number of balloons to the number of blue balloons equals the number of red balloons, which isn’t possible. So, this equation is False.

Summary:
- [tex]$ 62p = 186 $[/tex]: False
- [tex]$ 62 + p = 186 $[/tex]: True
- [tex]$ 186 + p = 62 $[/tex]: False