David, Archie and Christopher collected buttons in the ratio of 8 : 4 : 9. After Christopher gave ¹₅ to David and Archie, Christopher had 28 less buttons than David. The number of buttons that Archie had increased by 30%. How many buttons did David and Christopher have in the end?

	David	Archie	Christopher
Before	8 u	4 u	9 u
Change	+ 0.6 u	+ 1.2 u	- 1.8 u
After	8.6 u	5.2 u	7.2 u

Number of buttons that Christopher gave to David and Archie
= ¹₅ x 9 u
= 1.8 u

Number of buttons that Archie received from Christopher
= ³⁰₁₀₀ x 4 u
= 1.2 u

Number of buttons that David received from Christopher
= 1.8 u - 1.2 u
= 0.6 u

Number of less buttons that Christopher had less than David
= 8.6 u - 7.2 u 
= 1.4 u

1.4 u = 28

1 u = 28 ÷ 1.4 = 20

Number of buttons that David and Christopher had
= 8.6 u + 7.2 u
= 15.8 u
= 15.8 x 20
= 316

Answer(s): 316