In a jar, the ratio of the number of brown marbles to the number of grey marbles was 1 : 4. Each time, 3 brown and 6 grey marbles were taken out of the jar. A while later, only 180 grey marbles were left in the jar. What was the total number of marbles in the jar at first?
|
Brown marbles |
Grey marbles |
Before |
1x3 = 3 u |
4x3 = 12 u |
Change |
- 3 u |
- 6 u |
After |
0 |
180 |
Since there is no brown marbles left, this means that the number of brown marbles at first is the same as the number of brown marbles taken out.
Make the number of brown marbles at first and taken out the same. LCM of 1 and 3 is 3.
Number of grey marbles in the end
= 12 u - 6 u
= 6 u
6 u = 180
1 u = 180 ÷ 6 = 30
Total number of marbles in the jar at first
= 3 u + 12 u
= 15 u
= 15 x 30
= 450
Answer: 450