There were blue, silver and green balls in a jar. Sean put another 8 blue balls and 13 green balls in the jar, then the ratio of the number of silver balls to the number of green balls became 5 : 3. Then, he doubled the number of blue balls and removed 10 green balls. The ratio of the number of blue balls to silver balls became 2 : 1. He counted and found that there were a total of 152 balls left in the jar. Find the number of blue balls that he had at first.
|
Blue balls |
Silver balls |
Green balls |
Total |
Before |
5 u - 8 |
5 u |
3 u - 13 |
|
Change 1 |
+ 8 |
|
+ 13 |
|
After 1
|
1x5 = 5 u |
5 u |
3 u |
|
Change 2
|
+ 1x5 = 5 u |
|
- 10 |
|
After 2
|
2x5 = 10 u |
1x5 = 5 u |
3 u - 10 |
152 |
The number of silver balls remains unchanged. Make the number of silver balls the same. LCM of 1 and 5 is 5.
Total number of balls in the end
= 10 u + 5 u + 3 u - 10
= 18 u - 10
18 u - 10 = 152
18 u = 152 + 10
18 u = 162
1 u = 162 ÷ 18 = 9
Number of blue balls at first
= 5 u - 8
= 5 x 9 - 8
= 45 - 8
= 37
Answer(s): 37