There were white, red and purple balls in a box. Sean put another 10 white balls and 2 purple balls in the box, then the ratio of the number of red balls to the number of purple balls became 6 : 5. Then, he doubled the number of white balls and removed 22 purple balls. The ratio of the number of white balls to red balls became 2 : 1. He counted and found that there were a total of 116 balls left in the box. Find the number of white balls that he had in the end.
| |
White balls |
Red balls |
Purple balls |
Total |
| Before |
6 u - 10 |
6 u |
5 u - 2 |
|
| Change 1 |
+ 10 |
|
+ 2 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 22 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 22 |
116 |
The number of red balls remains unchanged. Make the number of red balls the same. LCM of 1 and 6 is 6.
Total number of balls in the end
= 12 u + 6 u + 5 u - 22
= 23 u - 22
23 u - 22 = 116
23 u = 116 + 22
23 u = 138
1 u = 138 ÷ 23 = 6
Number of white balls in the end
= 12 u
= 12 x 6
= 72
Answer(s): 72
