Ben had three bags of red beans, T, U and V and the mass of each bag of red beans was in the ratio 5 : 4 : 2. Ben decided to transfer 10% of red beans from Bag T into Bag U and 70% of red beans from Bag V into Bag U. Given that the mass of Bag U was 17.7 kg in the end, how many kilograms of red beans were transferred into Bag U?

	T	U	V
Before	5 u	4 u	2 u
Change 1	- 0.5 u	+ 0.5 u
Change 2		+ 1.4 u	- 1.4 u
After	4.5 u	5.9 u	0.6 u

Mass of red beans transferred from Bag T into Bag U
= 10% x 5 u
= ¹⁰₁₀₀ x 5 u
= 4.5 u

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

Mass of red beans in Bag U in the end
= 4 u + 0.5 u + 1.4 u
= 5.9 u

5.9 u = 17.7 

1 u = 17.7 ÷ 5.9 = 3

Mass of red beans transferred into Bag U
= 0.5 u + 1.4 u
= 1.9 u
= 1.9 x 3
= 5.7 kg

Answer(s): 5.7 kg