When using Many to Many relationships with Eloquent, the resulting model automatically gets a pivot
attribute assigned. Through that attribute you’re able to access pivot table columns.
Although by default there are only the keys in the pivot object. To get your columns in there too, you need to specify them when defining the relationship:
return $this->belongsToMany('Role')->withPivot('foo', 'bar');
If you need more help the task of configuring the relationships with Eloquent, let me know.
Edit
To query the price do this
$model->problems()->where('phone_problem', $problem->id)->first()->pivot->price