Cole had three bags of barley, N, P and Q and the mass of each bag of barley was in the ratio 3 : 5 : 3. Cole decided to transfer 40% of barley from Bag N into Bag P and 90% of barley from Bag Q into Bag P. Given that the mass of Bag P was 17.8 kg in the end, how many kilograms of barley were transferred into Bag P?
| |
N |
P |
Q |
| Before |
3 u |
5 u |
3 u |
| Change 1 |
- 1.2 u |
+ 1.2 u |
|
| Change 2 |
|
+ 2.7 u |
- 2.7 u |
| After |
1.8 u |
8.9 u |
0.3 u |
Mass of barley transferred from Bag N into Bag P
= 40% x 3 u
=
40100 x 3 u
= 1.8 u
Mass of barley transferred from Bag Q into Bag P
= 90% x 3 u
=
90100 x 3 u
= 2.7 u
Mass of barley in Bag P in the end
= 5 u + 1.2 u + 2.7 u
= 8.9 u
8.9 u = 17.8
1 u = 17.8 ÷ 8.9 = 2
Mass of barley transferred into Bag P
= 1.2 u + 2.7 u
= 3.9 u
= 3.9 x 2
= 7.8 kg
Answer(s): 7.8 kg
