Answer:
In C++:
#include <iostream>
using namespace std;
int main(){
    double quiz1, quiz2, quiz3, exam1, exam2, finalexam,quiz;
    cout<<"Quiz 1: "; cin>>quiz1; 
    cout<<"Quiz 2: "; cin>>quiz2; 
    cout<<"Quiz 3: "; cin>>quiz3; 
    cout<<"Exam 1: "; cin>>exam1; 
    cout<<"Exam 2: "; cin>>exam2; 
    cout<<"Final Exam: "; cin>>finalexam; 
    if(quiz1<=quiz2 && quiz1 <= quiz3){        quiz=(quiz2+quiz3)/2;    }
    else if(quiz2<=quiz1 && quiz2 <= quiz3){        quiz=(quiz1+quiz3)/2;    }
    else{         quiz=(quiz1+quiz2)/2;     }
    int weight = 0.20 * quiz + 0.30 * ((exam1 + exam2)/2) + 0.50 * finalexam;
    cout<<"Average Weight: "<<weight<<endl;
    if(weight>=91 && weight<=100){        cout<<"Letter Grade: A";    }
    else if(weight>=81 && weight<=90){        cout<<"Letter Grade: B";    }
    else if(weight>=70 && weight<=80){        cout<<"Letter Grade: C";    }
    else{        cout<<"Letter Grade: F";    }
    return 0;
}
Explanation:
See attachment for complete program where comments were used to explain difficult lines