Jeremy has a carton containing some green pears and yellow pears. If he adds in 18 green pears, 0.6 of the pears in the carton will be yellow pears. If he adds in 69 yellow pears, ³₄ of the pears in the carton will be green pears. How many pears are there in the carton?

	Yellow pears	Green pears	Yellow pears	Green pears
Before	3 u	2 u - 18	3 p - 69	1 p
Change		+ 18	+ 69
After	3 u	2 u	3 p	1 p

0.6 = ⁶₁₀ = ³₅

If he adds 18 green pears,
Number of green pears in the end
= 5 u - 3 u
= 2 u

If he adds 69 yellow pears,
Number of green pears 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 - 18 = 1 p
2 u = 1 p + 18 --- (2)

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

(2)_x3
6 u = 3 p + 54 --- (4)

(3) = (4)
6 p - 138 = 3 p + 54
6 p - 3 p = 138 + 54
3 p = 192

1 p = 192 ÷ 3 = 64

Number of pears at first
= 1 p + 3 p - 69
= 4 p - 69
= 4 x 64 - 69
= 256 - 69
= 187

Answer(s): 187