My code only outputs 0.00 when 'y' is entered. Clearly, I'm a beginner.

#include <iostream>
#include <iomanip> 
#include <string>

const double ADULTFEE = 18.00, CHILDFEE = 7.50, TRAINFEE = 6.00, BIRDFEE = 5.00;

using namespace std;

int main ()
{
    char reply = ' ';
    double adultNum = 0, childNum = 0, guestAdult = 0, guestChild = 0, trainNum = 0, birdNum = 0;
    double totalFee = 0;

    cout << "Welcome to Jake's Fee Calculator" << endl; 
    cout << "How many adults (age 14 or over) are in your party? ";
    cin >> adultNum;
    cout << "How many children (age 5 to 13) are in your party? ";
    cin >> childNum;
    cout << "Do you have a family membership? (y/n) ";
    cin >> reply;
    if (tolower(reply) == 'y')
    {
        cout << "How many adults in your party are guests? ";
        cin >> guestAdult;
        cout << "How many children (age 5 to 13) in your party are guests? ";
        cin >> guestChild;
        cout << "How many train tickets would you like? ";
        cin >> trainNum;
        cout << "How many bird show tickets would you like? ";
        cin >> birdNum;
    }
    else
    {
        cout << "How many train tickets would you like? ";
        cin >> trainNum;
        cout << "How many bird show tickets would you like? ";
        cin >> birdNum;
    }
    if (reply == 'y' && guestAdult > 2)
        totalFee = ((guestAdult - 2) * ADULTFEE) + (guestChild * CHILDFEE) + (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);

    else if (reply == 'y' && guestAdult == 2)
        totalFee = (guestChild * CHILDFEE) + (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);

    else if (reply == 'y' && (guestAdult == 1 && guestChild == 0))
        totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);

    else if (reply == 'y' && (guestAdult == 1 && guestChild == 1))
        totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);

    else if (reply == 'y' && (guestAdult == 0 && guestChild == 2))
        totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);

    else if (reply == 'y' && (guestAdult == 0 && guestChild > 2))
        totalFee = ((guestChild - 2) * CHILDFEE) + (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);

    else if (reply == 'y' && (guestAdult == 0 && guestChild == 1))
        totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);

    else if (reply == 'n')
        totalFee = (adultNum * ADULTFEE) + (childNum * CHILDFEE) + (trainNum * TRAINFEE) + (birdNum * BIRDFEE);

    cout << fixed << showpoint;
    cout << setprecision(2);
    cout << "Your total fee is $" << totalFee << endl;
    cout << "Thank you for using Jakes's Fee Calculator" << endl;

    system("pause");
    }

There are many opportunities in your code to enter the value 'y'; please tell us the complete input you typed in, what the output was, and what you expected the output to be.

And does it work when you enter 'n' ?

First, have a cleanup of your code. You may (must) replace your code from line 40 up to line 62 with the code below. That way, it could be cleaner to read (and debug) your code and it might help us—including yourself—solve your problem.

if (reply == 'y')
{
    switch (guestAdult)
    {
        case 0:
            if (guestChild == 1)
                totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);
            else if (guestChild == 2)
                totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);
            else if (guestChild > 2)
                totalFee = ((guestChild - 2) * CHILDFEE) + (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);
            break;
        case 1:
            if (guestChild == 0)
                totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);
            else if (guestChild == 1)
                totalFee = (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);
            break;
        case 2:
            totalFee = (guestChild * CHILDFEE) + (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);
            break;
        default:
            if( guestAdult > 2)
                totalFee = ((guestAdult - 2) * ADULTFEE) + (guestChild * CHILDFEE) + (((trainNum * TRAINFEE) + (birdNum * BIRDFEE))/2);
    }
}
else
    totalFee = (adultNum * ADULTFEE) + (childNum * CHILDFEE) + (trainNum * TRAINFEE) + (birdNum * BIRDFEE);
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