Gabriel, Charlie and Christopher collected buttons in the ratio of 8 : 9 : 6. After Christopher gave ⁷₁₀ to Gabriel and Charlie, Christopher had 272 less buttons than Gabriel. The number of buttons that Charlie had increased by 40%. How many buttons did Gabriel and Christopher have in the end?

	Gabriel	Charlie	Christopher
Before	8 u	9 u	6 u
Change	+ 0.6 u	+ 3.6 u	- 4.2 u
After	8.6 u	12.6 u	1.8 u

Number of buttons that Christopher gave to Gabriel and Charlie
= ⁷₁₀ x 6 u
= 4.2 u

Number of buttons that Charlie received from Christopher
= ⁴⁰₁₀₀ x 9 u
= 3.6 u

Number of buttons that Gabriel received from Christopher
= 4.2 u - 3.6 u
= 0.6 u

Number of less buttons that Christopher had less than Gabriel
= 8.6 u - 1.8 u 
= 6.8 u

6.8 u = 272

1 u = 272 ÷ 6.8 = 40

Number of buttons that Gabriel and Christopher had
= 8.6 u + 1.8 u
= 10.4 u
= 10.4 x 40
= 416

Answer(s): 416