从php中的json获取与另一项对应的项目

I want to read this JSON using PHP:

{
["person":{
   {"name":"Bill"},  
   {"age":"56"},
   {"city":"Houston"}
}],
["person":{  
   {"name":"Jack"},
   {"age":"45"},
   {"city":"Dallas"}
}],
["person":{
   {"name":"Henry"},
   {"age":"33"},
   {"city":"Atlanta"}
}]
}

Now I want to look for the person who's name is Jack and get the city he lives in. I know how to check for the name. But how can I get the corresponding city then?

I think this should make it:

$string = file_get_contents("persons.json");
$json = json_decode($string);

foreach ($json->person as $person) {
   if($person->name == "Jack")
  {
      $city = $person->city;
  }
}