Simon, Justin and Chester collected buttons in the ratio of 11 : 10 : 8. After Chester gave ³₅ to Simon and Justin, Chester had 273 less buttons than Simon. The number of buttons that Justin had increased by 35%. How many buttons did Simon and Chester have in the end?

	Simon	Justin	Chester
Before	11 u	10 u	8 u
Change	+ 1.3 u	+ 3.5 u	- 4.8 u
After	12.3 u	13.5 u	3.2 u

Number of buttons that Chester gave to Simon and Justin
= ³₅ x 8 u
= 4.8 u

Number of buttons that Justin received from Chester
= ³⁵₁₀₀ x 10 u
= 3.5 u

Number of buttons that Simon received from Chester
= 4.8 u - 3.5 u
= 1.3 u

Number of less buttons that Chester had less than Simon
= 12.3 u - 3.2 u 
= 9.1 u

9.1 u = 273

1 u = 273 ÷ 9.1 = 30

Number of buttons that Simon and Chester had
= 12.3 u + 3.2 u
= 15.5 u
= 15.5 x 30
= 465

Answer(s): 465