Tina had a collection of 1600 purple, brown and grey marbles. After Tina gave away 220 purple marbles, the number of purple marbles was 200 fewer than the number of brown marbles. Given that the number of grey marbles was twice as many as the number of brown marbles, how many purple marbles did Tina have at first?
| |
Purple marbles |
Brown marbles |
Grey marbles |
Total |
| Before |
1 u + 220 |
1 u + 200 |
2 u + 400 |
1600 |
| Change |
- 220 |
|
|
|
| After |
1 u |
1 u + 200 |
2 u + 400 |
|
Number of grey marbles in the end
= 2 x (1 u + 200)
= 2 u + 400
Total number of marbles at first
= 1 u + 220 + 1 u + 200 + 2 u + 400
= 4 u + 820
4 u + 820 = 1600
4 u = 1600 - 820
4 u = 780
1 u = 780 ÷ 4 = 195
Number of purple marbles that Tina had at first
= 1 u + 220
= 195 + 220
= 415
Answer(s): 415
