To answer this question, we will set an equation that describes the total cost of each plan after a certain number of visits.
Let n be the number of visits for which both plans cost the same, then we can set the following equation:
[tex]142+10n=46+22n\text{.}[/tex]Solving the above equation for n we get:
[tex]\begin{gathered} 142-46=22n-10n, \\ 96=12n, \\ \frac{96}{12}=n, \\ 8=n\text{.} \end{gathered}[/tex]Therefore, a person must make 8 visits for plans A and B to be equal in value.
Answer: 8.
