Cody had three bags of rice, V, W and X and the mass of each bag of rice was in the ratio 5 : 1 : 5. Cody decided to transfer 40% of rice from Bag V into Bag W and 70% of rice from Bag X into Bag W. Given that the mass of Bag W was 45.5 kg in the end, how many kilograms of rice were transferred into Bag W?
| |
V |
W |
X |
| Before |
5 u |
1 u |
5 u |
| Change 1 |
- 2 u |
+ 2 u |
|
| Change 2 |
|
+ 3.5 u |
- 3.5 u |
| After |
3 u |
6.5 u |
1.5 u |
Mass of rice transferred from Bag V into Bag W
= 40% x 5 u
=
40100 x 5 u
= 3 u
Mass of rice transferred from Bag X into Bag W
= 70% x 5 u
=
70100 x 5 u
= 3.5 u
Mass of rice in Bag W in the end
= 1 u + 2 u + 3.5 u
= 6.5 u
6.5 u = 45.5
1 u = 45.5 ÷ 6.5 = 7
Mass of rice transferred into Bag W
= 2 u + 3.5 u
= 5.5 u
= 5.5 x 7
= 38.5 kg
Answer(s): 38.5 kg
