The total number of balls in Box B, Box C and Box D was 163.
58 of the balls from Box B and 42 balls from Box C were removed. More balls were then added into Box D until the number of balls in it was quadrupled. The ratio of the number of balls in Box B to Box C to Box D became 3 : 2 : 4.
- How many less balls were there in Box C than Box B at first?
- Find the total number of balls in Box C and Box D in the end.
|
Box B |
Box C |
Box D |
Total |
Before |
8 u |
2 u + 42 |
1 u |
163 |
Change |
- 5 u |
- 42 |
+ 3 u |
|
After |
3 u |
|
4 u |
|
Comparing the balls in the end |
3 u |
2 u |
4 u |
|
(a)
Total number of balls at first
= 8 u + 2 u + 42 + 1 u
= 11 u + 42
11 u + 42 = 163
11 u = 163 - 42
11 u = 121
1 u = 121 ÷ 11 = 11
Number of less balls in Box C than Box B at first
= 8 u - (2 u + 42)
= 8 u - 2 u - 42
= 6 u - 42
= 6 x 11 - 42
= 66 - 42
= 24
(b)
Total number of balls in Box C and Box D in the end
= 2 u + 4 u
= 6 u
= 6 x 11
= 66
Answer(s): (a) 24; (b) 66