Question 1099986
.
<pre>
Let s = the number of the school seventh-graders and 
    e = the number of the school eight-graders.


We are given 


{{{(0.3*s)/(0.4*e)}}} = {{{21/32}}},   or, equivalently,

{{{(3*s)/(4*e)}}} = {{{21/32}}},

which implies 

{{{s/e}}} = {{{(21*4)/(32*3)}}} = {{{7/8}}}.



The problem asks about  {{{(s-0.3*s)/(e-0.4*e)}}}.   This ratio is 


{{{(s-0.3*s)/(e-0.4*e)}}} = {{{(s*(1-0.3))/(e*(1-0.4))}}} = {{{(0.7*s)/(0.6*e)}}} = {{{(0.7/0.6)*(s/e)}}} = {{{(0.7/0.6)*(7/8)}}} = {{{4.9/4.8}}} = {{{49/48}}}.



<U>Answer</U>.  The ratio under the question is  {{{49/48}}}.
</pre>