Usha had the same number of grey, red and purple buttons at first. After giving some grey and red buttons and 57 purple buttons away, Usha had 215 buttons left. There were 2 times as many grey buttons as red buttons left. The number of purple buttons left was 35 fewer than the number of grey buttons left. How many purple buttons did she have at first?
| |
Red |
Grey |
Purple |
Total |
| Before |
2 u + 22 |
2 u + 22 |
2 u + 22 |
|
| Change |
- 1 u - 22 |
- 22 |
- 57 |
|
| After |
1 u |
2 u |
2 u - 35 |
215 |
Usha had the same number of grey, red and purple buttons at first.
Total number of buttons in the end
= 1 u + 2 u + 2 u - 35
= 5 u - 35
5 u - 35 = 215
5 u = 215 + 35
5 u = 250
1 u = 250 ÷ 5 = 50
Number of purple buttons that Usha had at first
= 2 u - 35 + 57
= 2 u + 22
= 2 x 50 + 22
= 122
Answer(s): 122
