Jeremy has a carton containing some bunches of green grapes and bunches of red grapes. If he adds in 34 bunches of green grapes, 0.7 of the bunches of grapes in the carton will be bunches of red grapes. If he adds in 70 bunches of red grapes, ⁷₈ 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 green grapes	Bunches of red grapes	Bunches of green grapes
Before	7 u	3 u - 34	7 p - 70	1 p
Change		+ 34	+ 70
After	7 u	3 u	7 p	1 p

0.7 = ⁷₁₀ = ⁷₁₀

If he adds 34 bunches of green grapes,
Number of bunches of green grapes in the end
= 10 u - 7 u
= 3 u

If he adds 70 bunches of red grapes,
Number of bunches of green grapes in the end
= 8 p - 7 p
= 1 p

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

7 u = 7 p - 70 --- (1)

3 u - 34 = 1 p
3 u = 1 p + 34 --- (2)

Make u the same.
(1)_x3
21 u = 21 p - 210 --- (3)

(2)_x7
21 u = 7 p + 238 --- (4)

(3) = (4)
21 p - 210 = 7 p + 238
21 p - 7 p = 210 + 238
14 p = 448

1 p = 448 ÷ 14 = 32

Number of bunches of grapes at first
= 1 p + 7 p - 70
= 8 p - 70
= 8 x 32 - 70
= 256 - 70
= 186

Answer(s): 186