the equation is na+nb+nc+nd+ne=1500
where a=5 b=10 c=20 d=50 and e=100
remove the lowest common denominator of 5 to get
na+nb+nc+nd+ne=300
where a=1 b=2 c=4 d=10 and e =20
a is now irrelivent as n*a=n so
n+n(2)+n(4)+n(10)+n(20)=300
37n=300
n=300/37
n=8.108108 repeating