Jeremy has a carton containing some golden kiwis and green kiwis. If he adds in 31 golden kiwis, 0.7 of the kiwis in the carton will be green kiwis. If he adds in 51 green kiwis, ⁴₅ of the kiwis in the carton will be green kiwis. How many kiwis are there in the carton?

	Green kiwis	Golden kiwis	Green kiwis	Golden kiwis
Before	7 u	3 u - 31	4 p - 51	1 p
Change		+ 31	+ 51
After	7 u	3 u	4 p	1 p

0.7 = ⁷₁₀ = ⁷₁₀

If he adds 31 golden kiwis,
Number of golden kiwis in the end
= 10 u - 7 u
= 3 u

If he adds 51 green kiwis,
Number of golden kiwis in the end
= 5 p - 4 p
= 1 p

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

7 u = 4 p - 51 --- (1)

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

Make u the same.
(1)_x3
21 u = 12 p - 153 --- (3)

(2)_x7
21 u = 7 p + 217 --- (4)

(3) = (4)
12 p - 153 = 7 p + 217
12 p - 7 p = 153 + 217
5 p = 370

1 p = 370 ÷ 5 = 74

Number of kiwis at first
= 1 p + 4 p - 51
= 5 p - 51
= 5 x 74 - 51
= 370 - 51
= 319

Answer(s): 319