The total number of beads in Bag X, Bag Y and Bag Z was 43.
37 of the beads from Bag X and 3 beads from Bag Y were removed. More beads were then added into Bag Z until the number of beads in it was tripled. The ratio of the number of beads in Bag X to Bag Y to Bag Z became 4 : 2 : 3.
- How many less beads were there in Bag Y than Bag X at first?
- Find the total number of beads in Bag Y and Bag Z in the end.
|
Bag X |
Bag Y |
Bag Z |
Total |
Before |
7 u |
2 u + 3 |
1 u |
43 |
Change |
- 3 u |
- 3 |
+ 2 u |
|
After |
4 u |
|
3 u |
|
Comparing the beads in the end |
4 u |
2 u |
3 u |
|
(a)
Total number of beads at first
= 7 u + 2 u + 3 + 1 u
= 10 u + 3
10 u + 3 = 43
10 u = 43 - 3
10 u = 40
1 u = 40 ÷ 10 = 4
Number of less beads in Bag Y than Bag X at first
= 7 u - (2 u + 3)
= 7 u - 2 u - 3
= 5 u - 3
= 5 x 4 - 3
= 20 - 3
= 17
(b)
Total number of beads in Bag Y and Bag Z in the end
= 2 u + 3 u
= 5 u
= 5 x 4
= 20
Answer(s): (a) 17; (b) 20