¹₄ of the number of chickens that Farmer Peter had was equal to ³₄ of the number of chickens that Farmer Luis had. When Farmer Peter sold 300 of his chickens and Farmer Luis bought another 40, the ratio of the number of chickens that Farmer Peter had to the number of chickens Farmer Luis had become 2 : 3. What was the total number of chickens that the 2 farmers had at first?

	Make p the same (1) x 3 = (3)	Farmer Peter (1)	Farmer Luis (2)	Make p the same (2) x 2 = (4)
Before	36 u	12 u	4 u	8 u
Change	- 900	- 300	+ 40	+ 80
After	6 p	2 p	3 p	6 p

Make the numerators the same.
1x34x3 Farmer Peter's chickens = 3x14x1 Farmer Luis's chickens
312 Farmer Peter's chickens = 34 Farmer Luis's chickens

36 u - 900 = 8 u + 80
36 u - 8 u = 80 + 900
28 u = 980

1 u = 980 ÷ 28 = 35

Total number of chickens that the 2 farmers had
= 12 u + 4 u
= 16 u
= 16 x 35
= 560

Answer(s): 560