The number of red grapes is the same as the number of green grapes in a bag. After removing 1/4 of the grapes, there were 36 red grapes and 54 green grapes left in the bag. Then another 20 red grapes and 20 green grapes were removed and there were 5/12 of the grapes left in the end. How many red grapes were removed altogether?
r = removal red
g = removal green
let x = total of red grapes
y = total of green grapes
x + y = 1; x = y
1/4 = r + g
3/4 = (x - r) r(y - g)
5/12 = (x - r - 20) r (y - g - 20)
x - r = 36
y - g = 54
(x + y) (3/4) = 90
(x + y) (5/12) = 50
x + y = 120
2x = 120
x = 60
y = 60
60 - r = 36
r = 24 + 20
r = 44 red grapes were removed altogether