Question 643808
Let J be the fraction of the pizza that Judy ate and L be the fraction of the pizza that Linda ate.  Since Judy ate 3/4 the amount that Linda ate,
{{{J = (3/4)*L}}}
And since we assume that together they ate the whole pizza, 
{{{J + L = 1}}}
Substituting:
{{{(3/4)*L + L = 1}}}
{{{(3/4)*L + (4/4)*L = 1}}}
{{{((3+4)/4)*L = 1}}}
{{{(7/4)*L = 1}}}
{{{(4/7)*(7/4)*L = (4/7)*L}}}
{{{L = 4/7}}}
So Linda ate {{{4/7}}} of the pizza and Judy ate {{{3/7}}} of the pizza.
Therefore Linda should pay {{{21*(4/7)}}} = $12.00 and Judy should pay {{{21*(3/7)}}} = $9.00.