There were white, green and brown balls in a box. Sean put another 10 white balls and 7 brown balls in the box, then the ratio of the number of green balls to the number of brown balls became 6 : 5. Then, he doubled the number of white balls and removed 11 brown balls. The ratio of the number of white balls to green balls became 2 : 1. He counted and found that there were a total of 173 balls left in the box. Find the number of white balls that he had in the end.
| |
White balls |
Green balls |
Brown balls |
Total |
| Before |
6 u - 10 |
6 u |
5 u - 7 |
|
| Change 1 |
+ 10 |
|
+ 7 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 11 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 11 |
173 |
The number of green balls remains unchanged. Make the number of green balls the same. LCM of 1 and 6 is 6.
Total number of balls in the end
= 12 u + 6 u + 5 u - 11
= 23 u - 11
23 u - 11 = 173
23 u = 173 + 11
23 u = 184
1 u = 184 ÷ 23 = 8
Number of white balls in the end
= 12 u
= 12 x 8
= 96
Answer(s): 96
