Natalie had the same number of black, green and purple buttons at first. After giving some black and green buttons and 56 purple buttons away, Natalie had 225 buttons left. There were 4 times as many black buttons as green buttons left. The number of purple buttons left was 27 fewer than the number of black buttons left. How many purple buttons did she have at first?

	Green	Black	Purple	Total
Before	4 u + 29	4 u + 29	4 u + 29
Change	- 3 u - 29	- 29	- 56
After	1 u	4 u	4 u - 27	225

Natalie had the same number of black, green and purple buttons at first.

Total number of buttons in the end
= 1 u + 4 u + 4 u - 27
= 9 u - 27

9 u - 27 = 225
9 u = 225 + 27
9 u = 252

1 u = 252 ÷ 9 = 28

Number of purple buttons that Natalie had at first
= 4 u - 27 + 56
= 4 u + 29
= 4 x 28 + 29
= 141

Answer(s): 141