The total number of marbles in Bag K, Bag L and Bag M was 158.
37 of the marbles from Bag K and 2 marbles from Bag L were removed. More marbles were then added into Bag M until the number of marbles in it was doubled. The ratio of the number of marbles in Bag K to Bag L to Bag M became 4 : 5 : 2.
- How many less marbles were there in Bag L than Bag K at first?
- Find the total number of marbles in Bag L and Bag M in the end.
|
Bag K |
Bag L |
Bag M |
Total |
Before |
7 u |
5 u + 2 |
1 u |
158 |
Change |
- 3 u |
- 2 |
+ 1 u |
|
After |
4 u |
|
2 u |
|
Comparing the marbles in the end |
4 u |
5 u |
2 u |
|
(a)
Total number of marbles at first
= 7 u + 5 u + 2 + 1 u
= 13 u + 2
13 u + 2 = 158
13 u = 158 - 2
13 u = 156
1 u = 156 ÷ 13 = 12
Number of less marbles in Bag L than Bag K at first
= 7 u - (5 u + 2)
= 7 u - 5 u - 2
= 2 u - 2
= 2 x 12 - 2
= 24 - 2
= 22
(b)
Total number of marbles in Bag L and Bag M in the end
= 5 u + 2 u
= 7 u
= 7 x 12
= 84
Answer(s): (a) 22; (b) 84