The total number of marbles in Bag L, Bag M and Bag N was 102.
47 of the marbles from Bag L and 2 marbles from Bag M were removed. More marbles were then added into Bag N until the number of marbles in it was quadrupled. The ratio of the number of marbles in Bag L to Bag M to Bag N became 3 : 2 : 4.
- How many less marbles were there in Bag M than Bag L at first?
- Find the total number of marbles in Bag M and Bag N in the end.
|
Bag L |
Bag M |
Bag N |
Total |
Before |
7 u |
2 u + 2 |
1 u |
102 |
Change |
- 4 u |
- 2 |
+ 3 u |
|
After |
3 u |
|
4 u |
|
Comparing the marbles in the end |
3 u |
2 u |
4 u |
|
(a)
Total number of marbles at first
= 7 u + 2 u + 2 + 1 u
= 10 u + 2
10 u + 2 = 102
10 u = 102 - 2
10 u = 100
1 u = 100 ÷ 10 = 10
Number of less marbles in Bag M than Bag L at first
= 7 u - (2 u + 2)
= 7 u - 2 u - 2
= 5 u - 2
= 5 x 10 - 2
= 50 - 2
= 48
(b)
Total number of marbles in Bag M and Bag N in the end
= 2 u + 4 u
= 6 u
= 6 x 10
= 60
Answer(s): (a) 48; (b) 60