SOLUTION: Adam has some brown and green buttons in a box. If he were to remove some brown buttons, the ratio of brown to green buttons would then be 3 : 2. If he were to remove the same numb

Click here to see ALL problems on Percentage-and-ratio-word-problems

Question 1180523: Adam has some brown and green buttons in a box. If he were to remove some brown buttons, the ratio of brown to green buttons would then be 3 : 2. If he were to remove the same number of green buttons, the ratio of brown to green buttons would then be 14 : 1. Find the ratio of brown buttons to green buttons in the box.

Found 2 solutions by greenestamps, ankor@dixie-net.com:
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

b = # of brown buttons
g = # of green buttons
x = # of buttons removed

Removing x brown buttons makes the ratio of brown to green 3:2.
[1]

Removing x green buttons makes the ratio of brown to green 14:1.
[2]

"Cross multiply" in both equations

Substitute

ANSWER: The ratio of brown buttons to green buttons is 7:3

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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
=
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
=
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 = 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.
=
Cancel x

divide by .4
is the ratio