Zara had a collection of 1880 purple, blue and grey beads. After Zara gave away 250 purple beads, the number of purple beads was 110 fewer than the number of blue beads. Given that the number of grey beads was twice as many as the number of blue beads, how many purple beads did Zara have at first?
| |
Purple beads |
Blue beads |
Grey beads |
Total |
| Before |
1 u + 250 |
1 u + 110 |
2 u + 220 |
1880 |
| Change |
- 250 |
|
|
|
| After |
1 u |
1 u + 110 |
2 u + 220 |
|
Number of grey beads in the end
= 2 x (1 u + 110)
= 2 u + 220
Total number of beads at first
= 1 u + 250 + 1 u + 110 + 2 u + 220
= 4 u + 580
4 u + 580 = 1880
4 u = 1880 - 580
4 u = 1300
1 u = 1300 ÷ 4 = 325
Number of purple beads that Zara had at first
= 1 u + 250
= 325 + 250
= 575
Answer(s): 575
