Billy, Caden and Chester collected buttons in the ratio of 7 : 5 : 7. After Chester gave ⁴₅ to Billy and Caden, Chester had 204 less buttons than Billy. The number of buttons that Caden had increased by 20%. How many buttons did Billy and Chester have in the end?

	Billy	Caden	Chester
Before	7 u	5 u	7 u
Change	+ 4.6 u	+ 1 u	- 5.6 u
After	11.6 u	6 u	1.4 u

Number of buttons that Chester gave to Billy and Caden
= ⁴₅ x 7 u
= 5.6 u

Number of buttons that Caden received from Chester
= ²⁰₁₀₀ x 5 u
= 1 u

Number of buttons that Billy received from Chester
= 5.6 u - 1 u
= 4.6 u

Number of less buttons that Chester had less than Billy
= 11.6 u - 1.4 u 
= 10.2 u

10.2 u = 204

1 u = 204 ÷ 10.2 = 20

Number of buttons that Billy and Chester had
= 11.6 u + 1.4 u
= 13 u
= 13 x 20
= 260

Answer(s): 260