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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:

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