Jeremy has a carton containing some fuji apples and washington apples. If he adds in 36 fuji apples, 0.6 of the apples in the carton will be washington apples. If he adds in 69 washington apples, ³₄ of the apples in the carton will be green apples. How many apples are there in the carton?

	Washington apples	Fuji apples	Washington apples	Fuji apples
Before	3 u	2 u - 36	3 p - 69	1 p
Change		+ 36	+ 69
After	3 u	2 u	3 p	1 p

0.6 = ⁶₁₀ = ³₅

If he adds 36 fuji apples,
Number of fuji apples in the end
= 5 u - 3 u
= 2 u

If he adds 69 washington apples,
Number of fuji apples 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 - 69 --- (1)

2 u - 36 = 1 p
2 u = 1 p + 36 --- (2)

Make u the same.
(1)_x2
6 u = 6 p - 138 --- (3)

(2)_x3
6 u = 3 p + 108 --- (4)

(3) = (4)
6 p - 138 = 3 p + 108
6 p - 3 p = 138 + 108
3 p = 246

1 p = 246 ÷ 3 = 82

Number of apples at first
= 1 p + 3 p - 69
= 4 p - 69
= 4 x 82 - 69
= 328 - 69
= 259

Answer(s): 259