There were red, grey and white marbles in a bottle. Sean put another 5 red marbles and 10 white marbles in the bottle, then the ratio of the number of grey marbles to the number of white marbles became 4 : 3. Then, he doubled the number of red marbles and removed 11 white marbles. The ratio of the number of red marbles to grey marbles became 2 : 1. He counted and found that there were a total of 64 marbles left in the bottle. Find the number of red marbles that he had at first.
| |
Red marbles |
Grey marbles |
White marbles |
Total |
| Before |
4 u - 5 |
4 u |
3 u - 10 |
|
| Change 1 |
+ 5 |
|
+ 10 |
|
After 1
|
1x4 =
4 u |
4 u |
3 u |
|
Change 2
|
+ 1x4 =
4 u |
|
- 11 |
|
After 2
|
2x4 =
8 u |
1x4 =
4 u |
3 u - 11 |
64 |
The number of grey marbles remains unchanged. Make the number of grey marbles the same. LCM of 1 and 4 is 4.
Total number of marbles in the end
= 8 u + 4 u + 3 u - 11
= 15 u - 11
15 u - 11 = 64
15 u = 64 + 11
15 u = 75
1 u = 75 ÷ 15 = 5
Number of red marbles at first
= 4 u - 5
= 4 x 5 - 5
= 20 - 5
= 15
Answer(s): 15
