The total number of marbles in Bag X, Bag Y and Bag Z was 91.
78 of the marbles from Bag X and 19 marbles from Bag Y were removed. More marbles were then added into Bag Z until the number of marbles in it was tripled. The ratio of the number of marbles in Bag X to Bag Y to Bag Z became 1 : 3 : 3.
- How many less marbles were there in Bag Y than Bag X at first?
- Find the total number of marbles in Bag Y and Bag Z in the end.
|
Bag X |
Bag Y |
Bag Z |
Total |
Before |
8 u |
3 u + 19 |
1 u |
91 |
Change |
- 7 u |
- 19 |
+ 2 u |
|
After |
1 u |
|
3 u |
|
Comparing the marbles in the end |
1 u |
3 u |
3 u |
|
(a)
Total number of marbles at first
= 8 u + 3 u + 19 + 1 u
= 12 u + 19
12 u + 19 = 91
12 u = 91 - 19
12 u = 72
1 u = 72 ÷ 12 = 6
Number of less marbles in Bag Y than Bag X at first
= 8 u - (3 u + 19)
= 8 u - 3 u - 19
= 5 u - 19
= 5 x 6 - 19
= 30 - 19
= 11
(b)
Total number of marbles in Bag Y and Bag Z in the end
= 3 u + 3 u
= 6 u
= 6 x 6
= 36
Answer(s): (a) 11; (b) 36