Jeremy has a carton containing some washington apples and fuji apples. If he adds in 22 washington apples, 0.7 of the apples in the carton will be fuji apples. If he adds in 44 fuji apples, ³₄ of the apples in the carton will be green apples. How many apples are there in the carton?

	Fuji apples	Washington apples	Fuji apples	Washington apples
Before	7 u	3 u - 22	3 p - 44	1 p
Change		+ 22	+ 44
After	7 u	3 u	3 p	1 p

0.7 = ⁷₁₀ = ⁷₁₀

If he adds 22 washington apples,
Number of washington apples in the end
= 10 u - 7 u
= 3 u

If he adds 44 fuji apples,
Number of washington apples 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 - 44 --- (1)

3 u - 22 = 1 p
3 u = 1 p + 22 --- (2)

Make u the same.
(1)_x3
21 u = 9 p - 132 --- (3)

(2)_x7
21 u = 7 p + 154 --- (4)

(3) = (4)
9 p - 132 = 7 p + 154
9 p - 7 p = 132 + 154
2 p = 286

1 p = 286 ÷ 2 = 143

Number of apples at first
= 1 p + 3 p - 44
= 4 p - 44
= 4 x 143 - 44
= 572 - 44
= 528

Answer(s): 528