Question 774044
H = 100%, the apple juice
L = 16%, the fruit punch at 16% fruit juice
T = 51% fruit juice
C = 5 gal., the available apple juice
v = unknown gallons of the fruit punch to add


{{{(C*H+v*L)/(v+C)=T}}} SOLVE FOR v.
{{{CH+Lv=Tv+TC}}}
{{{Lv-Tv=TC-CH}}}
Multiply by -1, both sides,
{{{Tv-Lv=CH-CT}}}
{{{v(T-L)=C(H-T)}}}
{{{highlight(v=C((H-T)/(T-L)))}}}


SUBSTITUTE THE GIVEN VALUES TO COMPUTE v.