There were red, purple and blue balls in a box. Sean put another 6 red balls and 12 blue balls in the box, then the ratio of the number of purple balls to the number of blue balls became 6 : 5. Then, he doubled the number of red balls and removed 30 blue balls. The ratio of the number of red balls to purple balls became 2 : 1. He counted and found that there were a total of 177 balls left in the box. Find the number of red balls that he had in the end.
| |
Red balls |
Purple balls |
Blue balls |
Total |
| Before |
6 u - 6 |
6 u |
5 u - 12 |
|
| Change 1 |
+ 6 |
|
+ 12 |
|
After 1
|
1x6 =
6 u |
6 u |
5 u |
|
Change 2
|
+ 1x6 =
6 u |
|
- 30 |
|
After 2
|
2x6 =
12 u |
1x6 =
6 u |
5 u - 30 |
177 |
The number of purple balls remains unchanged. Make the number of purple balls the same. LCM of 1 and 6 is 6.
Total number of balls in the end
= 12 u + 6 u + 5 u - 30
= 23 u - 30
23 u - 30 = 177
23 u = 177 + 30
23 u = 207
1 u = 207 ÷ 23 = 9
Number of red balls in the end
= 12 u
= 12 x 9
= 108
Answer(s): 108
