Jeremy has a carton containing some bunches of green grapes and bunches of purple grapes. If he adds in 41 bunches of green grapes, 0.6 of the bunches of grapes in the carton will be bunches of purple grapes. If he adds in 54 bunches of purple 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 purple grapes	Bunches of green grapes	Bunches of purple grapes	Bunches of green grapes
Before	3 u	2 u - 41	3 p - 54	1 p
Change		+ 41	+ 54
After	3 u	2 u	3 p	1 p

0.6 = ⁶₁₀ = ³₅

If he adds 41 bunches of green grapes,
Number of bunches of green grapes in the end
= 5 u - 3 u
= 2 u

If he adds 54 bunches of purple grapes,
Number of bunches of green 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 - 54 --- (1)

2 u - 41 = 1 p
2 u = 1 p + 41 --- (2)

Make u the same.
(1)_x2
6 u = 6 p - 108 --- (3)

(2)_x3
6 u = 3 p + 123 --- (4)

(3) = (4)
6 p - 108 = 3 p + 123
6 p - 3 p = 108 + 123
3 p = 231

1 p = 231 ÷ 3 = 77

Number of bunches of grapes at first
= 1 p + 3 p - 54
= 4 p - 54
= 4 x 77 - 54
= 308 - 54
= 254

Answer(s): 254