The total number of beads in Bag V, Bag W and Bag X was 111.
45 of the beads from Bag V and 15 beads from Bag W were removed. More beads were then added into Bag X until the number of beads in it was tripled. The ratio of the number of beads in Bag V to Bag W to Bag X became 1 : 2 : 3.
- How many more beads were there in Bag V than Bag W at first?
- Find the total number of beads in Bag V and Bag X in the end.
|
Bag V |
Bag W |
Bag X |
Total |
Before |
5 u |
2 u + 15 |
1 u |
111 |
Change |
- 4 u |
- 15 |
+ 2 u |
|
After |
1 u |
|
3 u |
|
Comparing the beads in the end |
1 u |
2 u |
3 u |
|
(a)
Total number of beads at first
= 5 u + 2 u + 15 + 1 u
= 8 u + 15
8 u + 15 = 111
8 u = 111 - 15
8 u = 96
1 u = 96 ÷ 8 = 12
Number of more beads in Bag V than Bag W at first
= 5 u - (2 u + 15)
= 5 u - 2 u - 15
= 3 u - 15
= 3 x 12 - 15
= 36 - 15
= 21
(b)
Total number of beads in Bag V and Bag X in the end
= 1 u + 3 u
= 4 u
= 4 x 12
= 48
Answer(s): (a) 21; (b) 48