Elijah had three bags of barley, T, U and V and the mass of each bag of barley was in the ratio 1 : 5 : 2. Elijah decided to transfer 10% of barley from Bag T into Bag U and 70% of barley from Bag V into Bag U. Given that the mass of Bag U was 58.5 kg in the end, how many kilograms of barley were transferred into Bag U?

	T	U	V
Before	1 u	5 u	2 u
Change 1	- 0.1 u	+ 0.1 u
Change 2		+ 1.4 u	- 1.4 u
After	0.9 u	6.5 u	0.6 u

Mass of barley transferred from Bag T into Bag U
= 10% x 1 u
= ¹⁰₁₀₀ x 1 u
= 0.9 u

Mass of barley transferred from Bag V into Bag U
= 70% x 2 u
= ⁷⁰₁₀₀ x 2 u
= 1.4 u

Mass of barley in Bag U in the end
= 5 u + 0.1 u + 1.4 u
= 6.5 u

6.5 u = 58.5 

1 u = 58.5 ÷ 6.5 = 9

Mass of barley transferred into Bag U
= 0.1 u + 1.4 u
= 1.5 u
= 1.5 x 9
= 13.5 kg

Answer(s): 13.5 kg