The total number of balls in Box D, Box E and Box F was 120.
37 of the balls from Box D and 12 balls from Box E were removed. More balls were then added into Box F until the number of balls in it was tripled. The ratio of the number of balls in Box D to Box E to Box F became 4 : 4 : 3.
- How many more balls were there in Box D than Box E at first?
- Find the total number of balls in Box D and Box F in the end.
|
Box D |
Box E |
Box F |
Total |
Before |
7 u |
4 u + 12 |
1 u |
120 |
Change |
- 3 u |
- 12 |
+ 2 u |
|
After |
4 u |
|
3 u |
|
Comparing the balls in the end |
4 u |
4 u |
3 u |
|
(a)
Total number of balls at first
= 7 u + 4 u + 12 + 1 u
= 12 u + 12
12 u + 12 = 120
12 u = 120 - 12
12 u = 108
1 u = 108 ÷ 12 = 9
Number of more balls in Box D than Box E at first
= 7 u - (4 u + 12)
= 7 u - 4 u - 12
= 3 u - 12
= 3 x 9 - 12
= 27 - 12
= 15
(b)
Total number of balls in Box D and Box F in the end
= 4 u + 3 u
= 7 u
= 7 x 9
= 63
Answer(s): (a) 15; (b) 63