Question 323609
Let B be the sum of ages of the boys, G sum of ages of the girls.
Let Nb be the number of boys, Ng be the number of girls.
1.{{{B/Nb=10.6}}}
2.{{{G/Ng=10.1}}}
3.{{{(B+G)/(Nb+Ng)=10.5}}}
{{{Nb=60}}}
Then from eq. 1,
{{{B=60(10.6)}}}
{{{B=636}}}
From eq. 2, 
{{{G=10.1*Ng}}}
Substitute into eq. 3,
{{{(B+G)/(Nb+Ng)=10.5}}}
{{{B+G=10.5*Nb+10.5*Ng}}}
{{{B+10.1*Ng=10.5*Nb+10.5*Ng}}}
{{{10.6*Nb+10.1*Ng=10.5*Nb+10.5*Ng}}}
{{{0.1*Nb=0.4*Ng}}}
{{{Ng=Nb/4}}}
{{{Ng=60/4}}}
{{{highlight(Ng=15)}}}