Jeremy has a carton containing some washington apples and fuji apples. If he adds in 31 washington apples, 0.6 of the apples in the carton will be fuji apples. If he adds in 58 fuji apples, ⁷₈ 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	3 u	2 u - 31	7 p - 58	1 p
Change		+ 31	+ 58
After	3 u	2 u	7 p	1 p

0.6 = ⁶₁₀ = ³₅

If he adds 31 washington apples,
Number of washington apples in the end
= 5 u - 3 u
= 2 u

If he adds 58 fuji apples,
Number of washington apples in the end
= 8 p - 7 p
= 1 p

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

3 u = 7 p - 58 --- (1)

2 u - 31 = 1 p
2 u = 1 p + 31 --- (2)

Make u the same.
(1)_x2
6 u = 14 p - 116 --- (3)

(2)_x3
6 u = 3 p + 93 --- (4)

(3) = (4)
14 p - 116 = 3 p + 93
14 p - 3 p = 116 + 93
11 p = 209

1 p = 209 ÷ 11 = 19

Number of apples at first
= 1 p + 7 p - 58
= 8 p - 58
= 8 x 19 - 58
= 152 - 58
= 94

Answer(s): 94