Jeremy has a carton containing some bunches of red grapes and bunches of green grapes. If he adds in 39 bunches of red grapes, 0.7 of the bunches of grapes in the carton will be bunches of green grapes. If he adds in 41 bunches of green 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 green grapes	Bunches of red grapes	Bunches of green grapes	Bunches of red grapes
Before	7 u	3 u - 39	3 p - 41	1 p
Change		+ 39	+ 41
After	7 u	3 u	3 p	1 p

0.7 = ⁷₁₀ = ⁷₁₀

If he adds 39 bunches of red grapes,
Number of bunches of red grapes in the end
= 10 u - 7 u
= 3 u

If he adds 41 bunches of green grapes,
Number of bunches of red grapes in the end
= 4 p - 3 p
= 1 p

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

7 u = 3 p - 41 --- (1)

3 u - 39 = 1 p
3 u = 1 p + 39 --- (2)

Make u the same.
(1)_x3
21 u = 9 p - 123 --- (3)

(2)_x7
21 u = 7 p + 273 --- (4)

(3) = (4)
9 p - 123 = 7 p + 273
9 p - 7 p = 123 + 273
2 p = 396

1 p = 396 ÷ 2 = 198

Number of bunches of grapes at first
= 1 p + 3 p - 41
= 4 p - 41
= 4 x 198 - 41
= 792 - 41
= 751

Answer(s): 751