The total number of marbles in Bag L, Bag M and Bag N was 178.
38 of the marbles from Bag L and 24 marbles from Bag M were removed. More marbles were then added into Bag N until the number of marbles in it was tripled. The ratio of the number of marbles in Bag L to Bag M to Bag N became 5 : 5 : 3.
- How many more marbles were there in Bag L than Bag M at first?
- Find the total number of marbles in Bag L and Bag N in the end.
|
Bag L |
Bag M |
Bag N |
Total |
Before |
8 u |
5 u + 24 |
1 u |
178 |
Change |
- 3 u |
- 24 |
+ 2 u |
|
After |
5 u |
|
3 u |
|
Comparing the marbles in the end |
5 u |
5 u |
3 u |
|
(a)
Total number of marbles at first
= 8 u + 5 u + 24 + 1 u
= 14 u + 24
14 u + 24 = 178
14 u = 178 - 24
14 u = 154
1 u = 154 ÷ 14 = 11
Number of more marbles in Bag L than Bag M at first
= 8 u - (5 u + 24)
= 8 u - 5 u - 24
= 3 u - 24
= 3 x 11 - 24
= 33 - 24
= 9
(b)
Total number of marbles in Bag L and Bag N in the end
= 5 u + 3 u
= 8 u
= 8 x 11
= 88
Answer(s): (a) 9; (b) 88