The total number of marbles in Bag N, Bag P and Bag Q was 61.
58 of the marbles from Bag N and 6 marbles from Bag P were removed. More marbles were then added into Bag Q until the number of marbles in it was tripled. The ratio of the number of marbles in Bag N to Bag P to Bag Q became 3 : 2 : 3.
- How many more marbles were there in Bag N than Bag P at first?
- Find the total number of marbles in Bag N and Bag Q in the end.
|
Bag N |
Bag P |
Bag Q |
Total |
Before |
8 u |
2 u + 6 |
1 u |
61 |
Change |
- 5 u |
- 6 |
+ 2 u |
|
After |
3 u |
|
3 u |
|
Comparing the marbles in the end |
3 u |
2 u |
3 u |
|
(a)
Total number of marbles at first
= 8 u + 2 u + 6 + 1 u
= 11 u + 6
11 u + 6 = 61
11 u = 61 - 6
11 u = 55
1 u = 55 ÷ 11 = 5
Number of more marbles in Bag N than Bag P at first
= 8 u - (2 u + 6)
= 8 u - 2 u - 6
= 6 u - 6
= 6 x 5 - 6
= 30 - 6
= 24
(b)
Total number of marbles in Bag N and Bag Q in the end
= 3 u + 3 u
= 6 u
= 6 x 5
= 30
Answer(s): (a) 24; (b) 30