In a jar, the ratio of the number of grey balls to the number of purple balls was 1 : 3. Each time, 3 grey and 7 purple balls were taken out of the jar. A while later, only 108 purple balls were left in the jar. What was the total number of balls in the jar at first?
| |
Grey balls |
Purple balls |
| Before |
1x3 =
3 u |
3x3 =
9 u |
| Change |
- 3 u |
- 7 u |
| After |
0 |
108 |
Since there is no grey balls left, this means that the number of grey marbles at first is the same as the number of grey marbles taken out.
Make the number of grey balls at first and taken out the same. LCM of 1 and 3 is 3.
Number of purple balls in the end
= 9 u - 7 u
= 2 u
2 u = 108
1 u = 108 ÷ 2 = 54
Total number of balls in the jar at first
= 3 u + 9 u
= 12 u
= 12 x 54
= 648
Answer: 648
