Question 1180523
Adam has some brown and green buttons in a box.
let b = no. of brown buttons
let g = no. of green
 If he were to remove some brown buttons, the ratio of brown to green buttons would then be 3:2.
let x = no. brown buttons removed
{{{(b-x)/g}}} = {{{3/2}}}
cross multiply
3g = 2(b-x) 
3g = 2b - 2x
 If he were to remove the same number of green buttons, the ratio of brown to green buttons would then be 14:1.
let x = no. of green buttons removed
{{{b/(g-x)}}} = {{{14/1}}}
cross multiply
b = 14(g-x) 
b = 14g - 14x
in the first simplified equation replace b with (14g-14x)
3g = 2(14g-14x) - 2x
3g = 28g - 28x - 2x
3g - 28g = -30x
-25g = -30x
divide by -5
5g = 6x
g = {{{6/5}}}x
g = 1.2x
try to get b in terms of x also, replace g with (1.2x)
b = 14(1.2x) + 14x
b = 16.8x - 14x
b = 2.8x
 Find the ratio of brown buttons to green buttons in the box.
{{{b/g}}} = {{{(2.8x)/(1.2x)}}}
Cancel x
{{{2.8/1.2}}}
divide by .4
{{{7/3}}} is the ratio