¹₅ of the number of chickens that Farmer Jack had was equal to ³₄ of the number of chickens that Farmer Zeph had. When Farmer Jack sold 300 of his chickens and Farmer Zeph bought another 40, the ratio of the number of chickens that Farmer Jack had to the number of chickens Farmer Zeph had become 3 : 2. What was the total number of chickens that the 2 farmers had at first?

	Make p the same (1) x 2 = (3)	Farmer Jack (1)	Farmer Zeph (2)	Make p the same (2) x 3 = (4)
Before	30 u	15 u	4 u	12 u
Change	- 600	- 300	+ 40	+ 120
After	6 p	3 p	2 p	6 p

Make the numerators the same.
1x35x3 Farmer Jack's chickens = 3x14x1 Farmer Zeph's chickens
315 Farmer Jack's chickens = 34 Farmer Zeph's chickens

30 u - 600 = 12 u + 120
30 u - 12 u = 120 + 600
18 u = 720

1 u = 720 ÷ 18 = 40

Total number of chickens that the 2 farmers had
= 15 u + 4 u
= 19 u
= 19 x 40
= 760

Answer(s): 760