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Text Solution:

Let m = the number of airline miles that Maria has and v = the number of airline miles that Vito has. Since Maria has x more airline miles than her friend Vito, we can write equation 1 as the following:

$\Rightarrow m=v+x$

Since together Maria and Vito have a total of z airline miles, equation 2 can be the following:

$\Rightarrow v+m=z$

Substitute v + x from equation 1 for m in equation 2:

$\begin{array}{l}\Rightarrow v+m=z\\ \Rightarrow v+(v+x)=z\\ \Rightarrow 2v+x=z\\ \Rightarrow 2v=z-x\\ \Rightarrow v=\frac{z-x}{2}\end{array}$

Finally, we are asked what would happen if Vito earned $\frac{1}{2}w$ more airline miles, meaning we need to add this expression to Vito’s previous total airline miles:

$\begin{array}{l}\Rightarrow v=\frac{z-x}{2}+\frac{1}{2}w\\ \Rightarrow v=\frac{z-x}{2}+\frac{w}{2}\\ \Rightarrow v=\frac{z-x+w}{2}\text{airline miles}\end{array}$

LEARNING JOURNAL

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Was there a particular sticking point, breakdown in your logic or conceptual knowledge, bad habit, or careless mistake that led you to the wrong answer? At what point in your process did that error occur?

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