PSLE Emma had a box of purple marbles and blue marbles in the ratio 17 : 9. She removed an equal number of purple marbles and blue marbles from the box. The ratio of the number of purple marbles and blue marbles left in the box became 9 : 4. What percentage of the marbles were left in the box?
|
Purple marbles |
Blue marbles |
Difference |
Total |
Before |
17x5 = 85 u |
9x5 = 45 u |
8x5 = 40 u |
26x5 = 130 u |
Change |
- 13 u |
- 13 u |
|
|
After |
9x8 = 72 u |
4x8 = 32 u |
5x8 = 40 u |
13x8 = 104 u |
When Emma removed an equal number of purple marbles and blue marbles, the difference between the number of purple marbles and blue marbles at first and in the end remains the same.
LCM of 8 and 5 is 40.
Percentage of the marbles left in the box
=
104130 x 100%
= 45 x 100%
= 80%
Answer: 80%