There were green, pink and white balls in a box. Sean put another 9 green balls and 11 white balls in the box, then the ratio of the number of pink balls to the number of white balls became 4 : 3. Then, he doubled the number of green balls and removed 12 white balls. The ratio of the number of green balls to pink balls became 2 : 1. He counted and found that there were a total of 123 balls left in the box. Find the number of green balls that he had in the end.
| |
Green balls |
Pink balls |
White balls |
Total |
| Before |
4 u - 9 |
4 u |
3 u - 11 |
|
| Change 1 |
+ 9 |
|
+ 11 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 12 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 12 |
123 |
The number of pink balls remains unchanged. Make the number of pink balls the same. LCM of 1 and 4 is 4.
Total number of balls in the end
= 8 u + 4 u + 3 u - 12
= 15 u - 12
15 u - 12 = 123
15 u = 123 + 12
15 u = 135
1 u = 135 ÷ 15 = 9
Number of green balls in the end
= 8 u
= 8 x 9
= 72
Answer(s): 72
