Oliver had three bags of red beans, S, T and U and the mass of each bag of red beans was in the ratio 1 : 5 : 4. Oliver decided to transfer 10% of red beans from Bag S into Bag T and 90% of red beans from Bag U into Bag T. Given that the mass of Bag T was 52.2 kg in the end, how many kilograms of red beans were transferred into Bag T?

	S	T	U
Before	1 u	5 u	4 u
Change 1	- 0.1 u	+ 0.1 u
Change 2		+ 3.6 u	- 3.6 u
After	0.9 u	8.7 u	0.4 u

Mass of red beans transferred from Bag S into Bag T
= 10% x 1 u
= ¹⁰₁₀₀ x 1 u
= 0.9 u

Mass of red beans transferred from Bag U into Bag T
= 90% x 4 u
= ⁹⁰₁₀₀ x 4 u
= 3.6 u

Mass of red beans in Bag T in the end
= 5 u + 0.1 u + 3.6 u
= 8.7 u

8.7 u = 52.2 

1 u = 52.2 ÷ 8.7 = 6

Mass of red beans transferred into Bag T
= 0.1 u + 3.6 u
= 3.7 u
= 3.7 x 6
= 22.2 kg

Answer(s): 22.2 kg