A pet store holds training classes for dogs. The store has two different training programs. The first program charges a $35 membership fee and $5 for each class. The second program does not have a membership fee, but charges $10 for each class. For how many classes will the programs cost the same? If the variable c represents the number of classes, what is the other variable for the scenario? d, representing the number of dogs in each class h, representing the number of hours p, representing the number of programs t, representing the total cost.

Given, no. of classes is represented by c, no. of dogs is represented by d, no. of hours is represented by h, the no. of programs is represented by p and the total cost is represented by t.

The first program charges $35 membership fee and $5 for each class.

The second program charges only $10 for each class.

Now the total cost say [tex]t_{1}[/tex], for first program can be written in equation form as,

[tex]t_{1} =35+5c[/tex], here c is the no. of classes.

Similarly, the total cost say [tex]t_{2}[/tex] , for second program can be written in equation form as,

[tex]t_{2} =10c[/tex].

We have to find out the no. of classes for which the two programs cost the same.

according to the question,

[tex]t_{1} =t_{2}[/tex]

[tex]35+5c=10c\\10c-5c=35\\5c=35\\c=7[/tex]

Hence for 7 of classes the programs cost the same.

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