Check Credit Card Validity using Luhn Algorithm

Question

I tried to check the validation of credit card using Luhn algorithm, which works as the following steps:

1. Double every second digit from right to left. If do

Answer 1

Here's my implementation of the Luhn Formula.

/**
 * Runs the Luhn Equation on a user inputed CCN, which in turn
 * determines if it is a valid card number.
 * @param c A user inputed CCN.
 * @param cn The check number for the card.
 * @return If the card is valid based on the Luhn Equation.
 */
public boolean luhn (String c, char cn)
{
    String card = c;
    String checkString = "" + cn;
    int check = Integer.valueOf(checkString);

    //Drop the last digit.
    card = card.substring(0, ( card.length() - 1 ) );

    //Reverse the digits.
    String cardrev = new StringBuilder(card).reverse().toString();

    //Store it in an int array.
    char[] cardArray = cardrev.toCharArray();
    int[] cardWorking = new int[cardArray.length];
    int addedNumbers = 0;

    for (int i = 0; i < cardArray.length; i++)
    {
        cardWorking[i] = Character.getNumericValue( cardArray[i] );
    }

    //Double odd positioned digits (which are really even in our case, since index starts at 0).

    for (int j = 0; j < cardWorking.length; j++)
    {
        if ( (j % 2) == 0)
        {
            cardWorking[j] = cardWorking[j] * 2;
        }
    }

    //Subtract 9 from digits larger than 9.

    for (int k = 0; k < cardWorking.length; k++)
    {
        if (cardWorking[k] > 9)
        {
            cardWorking[k] = cardWorking[k] - 9;
        }
    }

    //Add all the numbers together.
    for (int l = 0; l < cardWorking.length; l++)
    {
        addedNumbers += cardWorking[l];
    }

    //Finally, check if the number we got from adding all the other numbers
    //when divided by ten has a remainder equal to the check number.
    if (addedNumbers % 10 == check)
    {
        return true;
    }
    else
    {           
        return false;
    }
}

I pass in the card as c which I get from a Scanner and store in card, and for cn I pass in checkNumber = card.charAt( (card.length() - 1) );.