PHP Script To Get The Actual Bitcoin Base On The USD Price and BTC Exchange Rate

This is a pretty classic programming question, but I think it is a very common one for the Bitcoin community, and would be helpful to have the code publicly available. My preference is for a php script.

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Bitpay publishes it's exchange rates here: https://bitpay.com/api/rates
If an item is $10 USD, how would I do the following?

1) extract the BTC/USD exchange rate from the array at this URL
2) Define the price, then divide by the exchange rate
3) Display the BTC price in an HTML page?

WARNING: RUN THE BELOW CODE ON THE LIVE SERVER (If possible let the server has https enabled)

<html>

<head><title>Bit calc</title>
</head>

<body>
<?php
$url = "https://bitpay.com/api/rates";

$json = file_get_contents($url);
$data = json_decode($json, TRUE);

$rate = $data[1]["rate"];
$usd_price = 10; # Let cost of elephant be 10$
echo $bitcoin_price = round( $usd_price / $rate , 8 );
?>

<ul>
<li>Price: <?php echo '='.$usd_price; ?> $ / <?php echo '='.$bitcoin_price; ?> BTC
</ul>

</body>

</html>