The total number of marbles in Bag M, Bag N and Bag P was 176.
58 of the marbles from Bag M and 8 marbles from Bag N were removed. More marbles were then added into Bag P until the number of marbles in it was doubled. The ratio of the number of marbles in Bag M to Bag N to Bag P became 3 : 5 : 2.
- How many more marbles were there in Bag M than Bag N at first?
- Find the total number of marbles in Bag M and Bag P in the end.
|
Bag M |
Bag N |
Bag P |
Total |
Before |
8 u |
5 u + 8 |
1 u |
176 |
Change |
- 5 u |
- 8 |
+ 1 u |
|
After |
3 u |
|
2 u |
|
Comparing the marbles in the end |
3 u |
5 u |
2 u |
|
(a)
Total number of marbles at first
= 8 u + 5 u + 8 + 1 u
= 14 u + 8
14 u + 8 = 176
14 u = 176 - 8
14 u = 168
1 u = 168 ÷ 14 = 12
Number of more marbles in Bag M than Bag N at first
= 8 u - (5 u + 8)
= 8 u - 5 u - 8
= 3 u - 8
= 3 x 12 - 8
= 36 - 8
= 28
(b)
Total number of marbles in Bag M and Bag P in the end
= 3 u + 2 u
= 5 u
= 5 x 12
= 60
Answer(s): (a) 28; (b) 60