The total number of marbles in Bag B, Bag C and Bag D was 43.
37 of the marbles from Bag B and 13 marbles from Bag C were removed. More marbles were then added into Bag D until the number of marbles in it was tripled. The ratio of the number of marbles in Bag B to Bag C to Bag D became 4 : 2 : 3.
- How many more marbles were there in Bag B than Bag C at first?
- Find the total number of marbles in Bag B and Bag D in the end.
|
Bag B |
Bag C |
Bag D |
Total |
Before |
7 u |
2 u + 13 |
1 u |
43 |
Change |
- 3 u |
- 13 |
+ 2 u |
|
After |
4 u |
|
3 u |
|
Comparing the marbles in the end |
4 u |
2 u |
3 u |
|
(a)
Total number of marbles at first
= 7 u + 2 u + 13 + 1 u
= 10 u + 13
10 u + 13 = 43
10 u = 43 - 13
10 u = 30
1 u = 30 ÷ 10 = 3
Number of more marbles in Bag B than Bag C at first
= 7 u - (2 u + 13)
= 7 u - 2 u - 13
= 5 u - 13
= 5 x 3 - 13
= 15 - 13
= 2
(b)
Total number of marbles in Bag B and Bag D in the end
= 4 u + 3 u
= 7 u
= 7 x 3
= 21
Answer(s): (a) 2; (b) 21