There were blue, green and purple balls in a box. Sean put another 9 blue balls and 14 purple balls in the box, then the ratio of the number of green balls to the number of purple balls became 4 : 3. Then, he doubled the number of blue balls and removed 26 purple balls. The ratio of the number of blue balls to green balls became 2 : 1. He counted and found that there were a total of 109 balls left in the box. Find the number of blue balls that he had in the end.
| |
Blue balls |
Green balls |
Purple balls |
Total |
| Before |
4 u - 9 |
4 u |
3 u - 14 |
|
| Change 1 |
+ 9 |
|
+ 14 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 26 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 26 |
109 |
The number of green balls remains unchanged. Make the number of green balls the same. LCM of 1 and 4 is 4.
Total number of balls in the end
= 8 u + 4 u + 3 u - 26
= 15 u - 26
15 u - 26 = 109
15 u = 109 + 26
15 u = 135
1 u = 135 ÷ 15 = 9
Number of blue balls in the end
= 8 u
= 8 x 9
= 72
Answer(s): 72
