The total number of balls in Box X, Box Y and Box Z was 156.
38 of the balls from Box X and 24 balls from Box Y were removed. More balls were then added into Box Z until the number of balls in it was quadrupled. The ratio of the number of balls in Box X to Box Y to Box Z became 5 : 3 : 4.
- How many less balls were there in Box Y than Box X at first?
- Find the total number of balls in Box Y and Box Z in the end.
|
Box X |
Box Y |
Box Z |
Total |
Before |
8 u |
3 u + 24 |
1 u |
156 |
Change |
- 3 u |
- 24 |
+ 3 u |
|
After |
5 u |
|
4 u |
|
Comparing the balls in the end |
5 u |
3 u |
4 u |
|
(a)
Total number of balls at first
= 8 u + 3 u + 24 + 1 u
= 12 u + 24
12 u + 24 = 156
12 u = 156 - 24
12 u = 132
1 u = 132 ÷ 12 = 11
Number of less balls in Box Y than Box X at first
= 8 u - (3 u + 24)
= 8 u - 3 u - 24
= 5 u - 24
= 5 x 11 - 24
= 55 - 24
= 31
(b)
Total number of balls in Box Y and Box Z in the end
= 3 u + 4 u
= 7 u
= 7 x 11
= 77
Answer(s): (a) 31; (b) 77