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.
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+128475 We have two equations
(G - x ) / B = 3/2 ⇒ 2(G - x) = 3B ⇒ 2G - 2x = 3B ⇒ (28/3)G - (28/3)x = 14B (1)
G /( B - x) = 14 ⇒ G = 14(B - x) ⇒ G = 14B - 14x ⇒ 14B = G + 14x (2)
Equating (1) and (2)
(28/3)G - (28/3)x = G + 14x
(25/3)G = (70/3)x
25G = 70x
LCM 25, 70 = 350
25G =350 and 70x = 350
We have an equality when G = 14 and x = 5
So
2G - 2x = 3B
28 - 10 = 3B
18 = 3B
6 = B
Proof
(14-5) / 6 = 9/6 = 3/2
and
14 / ( 6 - 5) = 14 / 1
Ratio of B /G = 14 / 6 = 7 / 3
