The total number of marbles in Box F, Box G and Box H was 144.
78 of the marbles from Box F and 27 marbles from Box G were removed. More marbles were then added into Box H until the number of marbles in it was tripled. The ratio of the number of marbles in Box F to Box G to Box H became 1 : 4 : 3.
- How many less marbles were there in Box G than Box F at first?
- Find the total number of marbles in Box G and Box H in the end.
|
Box F |
Box G |
Box H |
Total |
Before |
8 u |
4 u + 27 |
1 u |
144 |
Change |
- 7 u |
- 27 |
+ 2 u |
|
After |
1 u |
|
3 u |
|
Comparing the marbles in the end |
1 u |
4 u |
3 u |
|
(a)
Total number of marbles at first
= 8 u + 4 u + 27 + 1 u
= 13 u + 27
13 u + 27 = 144
13 u = 144 - 27
13 u = 117
1 u = 117 ÷ 13 = 9
Number of less marbles in Box G than Box F at first
= 8 u - (4 u + 27)
= 8 u - 4 u - 27
= 4 u - 27
= 4 x 9 - 27
= 36 - 27
= 9
(b)
Total number of marbles in Box G and Box H in the end
= 4 u + 3 u
= 7 u
= 7 x 9
= 63
Answer(s): (a) 9; (b) 63