Esther had a collection of 1900 white, red and purple marbles. After Esther gave away 330 white marbles, the number of white marbles was 180 fewer than the number of red marbles. Given that the number of purple marbles was five times as many as the number of red marbles, how many white marbles did Esther have at first?
| |
White marbles |
Red marbles |
Purple marbles |
Total |
| Before |
1 u + 330 |
1 u + 180 |
5 u + 900 |
1900 |
| Change |
- 330 |
|
|
|
| After |
1 u |
1 u + 180 |
5 u + 900 |
|
Number of purple marbles in the end
= 5 x (1 u + 180)
= 5 u + 900
Total number of marbles at first
= 1 u + 330 + 1 u + 180 + 5 u + 900
= 7 u + 1410
7 u + 1410 = 1900
7 u = 1900 - 1410
7 u = 490
1 u = 490 ÷ 7 = 70
Number of white marbles that Esther had at first
= 1 u + 330
= 70 + 330
= 400
Answer(s): 400
