The total number of marbles in Bag P, Bag Q and Bag R was 198.
38 of the marbles from Bag P and 42 marbles from Bag Q were removed. More marbles were then added into Bag R until the number of marbles in it was tripled. The ratio of the number of marbles in Bag P to Bag Q to Bag R became 5 : 4 : 3.
- How many less marbles were there in Bag Q than Bag P at first?
- Find the total number of marbles in Bag Q and Bag R in the end.
|
Bag P |
Bag Q |
Bag R |
Total |
Before |
8 u |
4 u + 42 |
1 u |
198 |
Change |
- 3 u |
- 42 |
+ 2 u |
|
After |
5 u |
|
3 u |
|
Comparing the marbles in the end |
5 u |
4 u |
3 u |
|
(a)
Total number of marbles at first
= 8 u + 4 u + 42 + 1 u
= 13 u + 42
13 u + 42 = 198
13 u = 198 - 42
13 u = 156
1 u = 156 ÷ 13 = 12
Number of less marbles in Bag Q than Bag P at first
= 8 u - (4 u + 42)
= 8 u - 4 u - 42
= 4 u - 42
= 4 x 12 - 42
= 48 - 42
= 6
(b)
Total number of marbles in Bag Q and Bag R in the end
= 4 u + 3 u
= 7 u
= 7 x 12
= 84
Answer(s): (a) 6; (b) 84