In a bag, the ratio of the number of pink marbles to the number of grey marbles was 1 : 3. Each time, 4 pink and 6 grey marbles were taken out of the bag. A while later, only 90 grey marbles were left in the bag. What was the total number of marbles in the bag at first?
|
Pink marbles |
Grey marbles |
Before |
1x4 = 4 u |
3x4 = 12 u |
Change |
- 4 u |
- 6 u |
After |
0 |
90 |
Since there is no pink marbles left, this means that the number of pink marbles at first is the same as the number of pink marbles taken out.
Make the number of pink marbles at first and taken out the same. LCM of 1 and 4 is 4.
Number of grey marbles in the end
= 12 u - 6 u
= 6 u
6 u = 90
1 u = 90 ÷ 6 = 15
Total number of marbles in the bag at first
= 4 u + 12 u
= 16 u
= 16 x 15
= 240
Answer: 240