The total number of marbles in Box M, Box N and Box P was 135.
47 of the marbles from Box M and 3 marbles from Box N were removed. More marbles were then added into Box P until the number of marbles in it was doubled. The ratio of the number of marbles in Box M to Box N to Box P became 3 : 3 : 2.
- How many more marbles were there in Box M than Box N at first?
- Find the total number of marbles in Box M and Box P in the end.
|
Box M |
Box N |
Box P |
Total |
Before |
7 u |
3 u + 3 |
1 u |
135 |
Change |
- 4 u |
- 3 |
+ 1 u |
|
After |
3 u |
|
2 u |
|
Comparing the marbles in the end |
3 u |
3 u |
2 u |
|
(a)
Total number of marbles at first
= 7 u + 3 u + 3 + 1 u
= 11 u + 3
11 u + 3 = 135
11 u = 135 - 3
11 u = 132
1 u = 132 ÷ 11 = 12
Number of more marbles in Box M than Box N at first
= 7 u - (3 u + 3)
= 7 u - 3 u - 3
= 4 u - 3
= 4 x 12 - 3
= 48 - 3
= 45
(b)
Total number of marbles in Box M and Box P in the end
= 3 u + 2 u
= 5 u
= 5 x 12
= 60
Answer(s): (a) 45; (b) 60