The total number of marbles in Box V, Box W and Box X was 138.
38 of the marbles from Box V and 21 marbles from Box W were removed. More marbles were then added into Box X until the number of marbles in it was tripled. The ratio of the number of marbles in Box V to Box W to Box X became 5 : 4 : 3.
- How many less marbles were there in Box W than Box V at first?
- Find the total number of marbles in Box W and Box X in the end.
|
Box V |
Box W |
Box X |
Total |
Before |
8 u |
4 u + 21 |
1 u |
138 |
Change |
- 3 u |
- 21 |
+ 2 u |
|
After |
5 u |
|
3 u |
|
Comparing the marbles in the end |
5 u |
4 u |
3 u |
|
(a)
Total number of marbles at first
= 8 u + 4 u + 21 + 1 u
= 13 u + 21
13 u + 21 = 138
13 u = 138 - 21
13 u = 117
1 u = 117 ÷ 13 = 9
Number of less marbles in Box W than Box V at first
= 8 u - (4 u + 21)
= 8 u - 4 u - 21
= 4 u - 21
= 4 x 9 - 21
= 36 - 21
= 15
(b)
Total number of marbles in Box W and Box X in the end
= 4 u + 3 u
= 7 u
= 7 x 9
= 63
Answer(s): (a) 15; (b) 63