Ryan had three bags of barley, P, Q and R and the mass of each bag of barley was in the ratio 2 : 3 : 3. Ryan decided to transfer 10% of barley from Bag P into Bag Q and 90% of barley from Bag R into Bag Q. Given that the mass of Bag Q was 53.1 kg in the end, how many kilograms of barley were transferred into Bag Q?
| |
P |
Q |
R |
| Before |
2 u |
3 u |
3 u |
| Change 1 |
- 0.2 u |
+ 0.2 u |
|
| Change 2 |
|
+ 2.7 u |
- 2.7 u |
| After |
1.8 u |
5.9 u |
0.3 u |
Mass of barley transferred from Bag P into Bag Q
= 10% x 2 u
=
10100 x 2 u
= 1.8 u
Mass of barley transferred from Bag R into Bag Q
= 90% x 3 u
=
90100 x 3 u
= 2.7 u
Mass of barley in Bag Q in the end
= 3 u + 0.2 u + 2.7 u
= 5.9 u
5.9 u = 53.1
1 u = 53.1 ÷ 5.9 = 9
Mass of barley transferred into Bag Q
= 0.2 u + 2.7 u
= 2.9 u
= 2.9 x 9
= 26.1 kg
Answer(s): 26.1 kg
