Cathy has a bag containing some purple and blue marbles. If she removes 4 purple marbles, 20% of the marbles in the bag are blue. If she adds another 9 blue marbles, 50% of the marbles in the bag are blue. How many purple marbles are in the bag?
| |
Purple marbles |
Blue marbles |
| Before |
4 u + 4 |
1 u |
| Change 1 |
- 4 |
|
| After 1 |
4x1 =
4 u |
1x1 =
1 u |
| Change 2 |
|
+ 9 |
| After 2 |
1x4 =
4 u |
1x4 =
4 u |
20% =
20100 =
1550% =
50100 =
12The number of purple marbles remains unchanged at the second change when she adds another 9 blue marbles. Make the number of purple marbles the same at the second change. LCM of 4 and 1 is 4.
Number of blue marbles added
= 4 u - 1 u
= 3 u
3 u = 9
1 u = 9 ÷ 3 = 3
Number of purple marbles at first
= 4 u + 4
= 4 x 3 + 4
= 12 + 4
= 16
Answer(s): 16
