Xavier had three bags of oats, P, Q and R and the mass of each bag of oats was in the ratio 3 : 2 : 2. Xavier decided to transfer 30% of oats from Bag P into Bag Q and 60% of oats from Bag R into Bag Q. Given that the mass of Bag Q was 24.6 kg in the end, how many kilograms of oats were transferred into Bag Q?
| |
P |
Q |
R |
| Before |
3 u |
2 u |
2 u |
| Change 1 |
- 0.9 u |
+ 0.9 u |
|
| Change 2 |
|
+ 1.2 u |
- 1.2 u |
| After |
2.1 u |
4.1 u |
0.8 u |
Mass of oats transferred from Bag P into Bag Q
= 30% x 3 u
=
30100 x 3 u
= 2.1 u
Mass of oats transferred from Bag R into Bag Q
= 60% x 2 u
=
60100 x 2 u
= 1.2 u
Mass of oats in Bag Q in the end
= 2 u + 0.9 u + 1.2 u
= 4.1 u
4.1 u = 24.6
1 u = 24.6 ÷ 4.1 = 6
Mass of oats transferred into Bag Q
= 0.9 u + 1.2 u
= 2.1 u
= 2.1 x 6
= 12.6 kg
Answer(s): 12.6 kg
