php calculating total cases from 2 different inputs

so, this seems really simple, but I have been scratching my head for about an hour now.
Simple math, but I cannot replicate with code.
1 case = 4 bags, 4 bags = 8 bottles, 8 bottles = 1 case.

<form method="post">
    <input type="text" name="cases" placeholder="cases...">
    <input type="text" name="bottles" placeholder="bottles...">
    <button name="submit">submit</button>
    <?php echo $output; ?>
</form>

if(isset($_POST['submit'])){
    $cases = $_POST['cases'];
    $bottles = $_POST['bottles'];
    $xcases = $cases * 4;
    $xbottles = $bottles / 4;
    $c = $xbottles + $xcases;
    $output = $xbottles;
}

I’ve tried changing the math around, but just can’t seem to get it right.