Question 1180523
<br>
b = # of brown buttons
g = # of green buttons
x = # of buttons removed<br>
Removing x brown buttons makes the ratio of brown to green 3:2.
{{{(b-x)/g=3/2}}}  [1]<br>
Removing x green buttons makes the ratio of brown to green 14:1.
{{{b/(g-x)=14/1}}}  [2]<br>
"Cross multiply" in both equations<br>
{{{3g=2(b-x)}}}
{{{b=14(g-x)}}}<br>
Substitute<br>
{{{3g=2(14(g-x)-x)=28g-28x-2x=28g-30x}}}
{{{30x=25g}}}
{{{x=(5/6)g}}}<br>
{{{b=14(g-x)=14((1/6)g) = (7/3)g}}}
{{{b/g=7/3}}}<br>
ANSWER: The ratio of brown buttons to green buttons is 7:3<br>