Jeremy has a carton containing some bunches of purple grapes and bunches of red grapes. If he adds in 50 bunches of purple grapes, 0.6 of the bunches of grapes in the carton will be bunches of red grapes. If he adds in 60 bunches of red grapes, ³₄ of the bunches of grapes in the carton will be green bunches of grapes. How many bunches of grapes are there in the carton?

	Bunches of red grapes	Bunches of purple grapes	Bunches of red grapes	Bunches of purple grapes
Before	3 u	2 u - 50	3 p - 60	1 p
Change		+ 50	+ 60
After	3 u	2 u	3 p	1 p

0.6 = ⁶₁₀ = ³₅

If he adds 50 bunches of purple grapes,
Number of bunches of purple grapes in the end
= 5 u - 3 u
= 2 u

If he adds 60 bunches of red grapes,
Number of bunches of purple grapes in the end
= 4 p - 3 p
= 1 p

The number of each type in both scenarios remain unchanged at first.

3 u = 3 p - 60 --- (1)

2 u - 50 = 1 p
2 u = 1 p + 50 --- (2)

Make u the same.
(1)_x2
6 u = 6 p - 120 --- (3)

(2)_x3
6 u = 3 p + 150 --- (4)

(3) = (4)
6 p - 120 = 3 p + 150
6 p - 3 p = 120 + 150
3 p = 270

1 p = 270 ÷ 3 = 90

Number of bunches of grapes at first
= 1 p + 3 p - 60
= 4 p - 60
= 4 x 90 - 60
= 360 - 60
= 300

Answer(s): 300