Q:

Check a radio button by clicking the  associated with it

I have a set of elements like this:
<div class="input-group">
    <span class="input-group-addon">
            <input type="radio" name="location-radio" />
     </span>
    <a data-id="" class="list-group-item location-list-group-item">
            <span class="badge">0</span>Takeaway
    </a>
</div>

Whenever an  element with the class .location-list-group-item is clicked the radio button above it must be checked.
The code I am using to do this is:
$(function(){
    $(".location-list-group-item").click(function(){
        alert("Hit");
        $(event.target).prev('span.input-group-addon:nth-child(1)').prop("checked", true)
    });
}); 

The click event is working I just cant get the box to check.
I have tried many ways so far but none seem to work.
I have the latest version of jquery and I am at a loss.
EDIT: 
Thank you all for your responses, you all helped me learn more about selecting elements :D 

A:

Try this,
$(function(){
    $(".location-list-group-item").click(function(){   
        $(this).prev().children('input[type=radio]').prop("checked", true);
    });
}); 

DEMO

