Given:
a.) They have played 3 of their 15 games.
b.) They create a model to represent x, the number of games their team has left to play.
Let's first determine the value of x to be able to counter-check their models.
[tex]\text{ x = Total number of games - Number of games played}[/tex][tex]\text{ = 15 - 3}[/tex][tex]\text{ x = 12}[/tex]Therefore, for us to determine if their models are correct, x must be equal to 12.
a.) Analyzing Elijah's Model.
His model, in equation, appears to be:
[tex]\text{ x + 3 = 15}[/tex]Let's determine the value of x to check if his model is correct.
[tex]\text{ x + 3 = 15}[/tex][tex]\text{ x = 15 - 3}[/tex][tex]\text{ x = 12}[/tex]Therefore, Elijah's model is correct.
b.) Analyzing Jonathan's Model.
His model, in equation, appears to be:
[tex]\text{ 3x = 15}[/tex]Let's determine the value of x to check if his model is correct.
[tex]\text{ 3x = 15}[/tex][tex]\text{ }\frac{\text{3x}}{3}\text{ = }\frac{\text{15}}{3}[/tex][tex]\text{ x = 5}[/tex]Jonathan's model is incorrect. For it to be correct, he should have only an x and a 3 in the top bar for it to generate the equation below.
[tex]\text{ x + 3 = 15}[/tex][tex]\text{ x = 15 - 3 }\rightarrow\text{ x = 12}[/tex]