There were black, white and grey marbles in a jar. Sean put another 4 black marbles and 15 grey marbles in the jar, then the ratio of the number of white marbles to the number of grey marbles became 6 : 5. Then, he doubled the number of black marbles and removed 11 grey marbles. The ratio of the number of black marbles to white marbles became 2 : 1. He counted and found that there were a total of 173 marbles left in the jar. Find the number of black marbles that he had in the end.
| |
Black marbles |
White marbles |
Grey marbles |
Total |
| Before |
6 u - 4 |
6 u |
5 u - 15 |
|
| Change 1 |
+ 4 |
|
+ 15 |
|
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 white marbles remains unchanged. Make the number of white marbles the same. LCM of 1 and 6 is 6.
Total number of marbles 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 black marbles in the end
= 12 u
= 12 x 8
= 96
Answer(s): 96
