PSLE Opal had a bag of brown marbles and red marbles in the ratio 13 : 7. She removed an equal number of brown marbles and red marbles from the bag. The ratio of the number of brown marbles and red marbles left in the bag became 3 : 1. What percentage of the marbles were left in the bag?
|
Brown marbles |
Red marbles |
Difference |
Total |
Before |
13x1 = 13 u |
7x1 = 7 u |
6x1 = 6 u |
20x1 = 20 u |
Change |
- 4 u |
- 4 u |
|
|
After |
3x3 = 9 u |
1x3 = 3 u |
2x3 = 6 u |
4x3 = 12 u |
When Opal removed an equal number of brown marbles and red marbles, the difference between the number of brown marbles and red marbles at first and in the end remains the same.
LCM of 6 and 2 is 6.
Percentage of the marbles left in the bag
=
1220 x 100%
= 35 x 100%
= 60%
Answer: 60%