Jean had a collection of 1750 purple, gold and red marbles. After Jean gave away 280 purple marbles, the number of purple marbles was 120 fewer than the number of gold marbles. Given that the number of red marbles was four times as many as the number of gold marbles, how many purple marbles did Jean have at first?
| |
Purple marbles |
Gold marbles |
Red marbles |
Total |
| Before |
1 u + 280 |
1 u + 120 |
4 u + 480 |
1750 |
| Change |
- 280 |
|
|
|
| After |
1 u |
1 u + 120 |
4 u + 480 |
|
Number of red marbles in the end
= 4 x (1 u + 120)
= 4 u + 480
Total number of marbles at first
= 1 u + 280 + 1 u + 120 + 4 u + 480
= 6 u + 880
6 u + 880 = 1750
6 u = 1750 - 880
6 u = 870
1 u = 870 ÷ 6 = 145
Number of purple marbles that Jean had at first
= 1 u + 280
= 145 + 280
= 425
Answer(s): 425
