<PRE><B>Question 274427</B>
Box A has 9 green balls and 4 red balls.
 Box B has 12 green balls and 5 red balls.
 Suppose you want the fraction of green balls in box A to equal the fraction of red balls in box B.
 How many green balls must you move from Box A to Box B?
:
Let x = no. of green balls moved
:
{{{red/green}}} 
:
{{{4/(9-x)}}} = {{{(12+x)/5}}}; (relationship is reversed)
;
Cross multiply
(9-x)(12+x) = 4 * 5
FOIL
108 + 9x - 12x - x^2 = 20
;
Arrange as a quadratic dquation
-x^2 - 3x + 108 - 20 = 0
-x^2 - 3x + 88 = 0
Multiply by -1
x^2 + 3x - 88 = 0
Factor
(x+11)(x-8) = 0
positive solution
x = 8 balls are moved
:
:
See if that is true
{{{4/(9-8)}}} = {{{(12+8)/5}}} which is: {{{4/1}}} = {{{20/5}}}</PRE>