The total number of balls in Box W, Box X and Box Y was 197.
78 of the balls from Box W and 41 balls from Box X were removed. More balls were then added into Box Y until the number of balls in it was quadrupled. The ratio of the number of balls in Box W to Box X to Box Y became 1 : 4 : 4.
- How many more balls were there in Box W than Box X at first?
- Find the total number of balls in Box W and Box Y in the end.
|
Box W |
Box X |
Box Y |
Total |
Before |
8 u |
4 u + 41 |
1 u |
197 |
Change |
- 7 u |
- 41 |
+ 3 u |
|
After |
1 u |
|
4 u |
|
Comparing the balls in the end |
1 u |
4 u |
4 u |
|
(a)
Total number of balls at first
= 8 u + 4 u + 41 + 1 u
= 13 u + 41
13 u + 41 = 197
13 u = 197 - 41
13 u = 156
1 u = 156 ÷ 13 = 12
Number of more balls in Box W than Box X at first
= 8 u - (4 u + 41)
= 8 u - 4 u - 41
= 4 u - 41
= 4 x 12 - 41
= 48 - 41
= 7
(b)
Total number of balls in Box W and Box Y in the end
= 1 u + 4 u
= 5 u
= 5 x 12
= 60
Answer(s): (a) 7; (b) 60