There are 25% more purple buttons than gold buttons in a bag. After Sam removed 20% of the purple buttons and increased the number of gold buttons by 10%, there are now 28 fewer purple buttons than gold buttons. Find the number of gold buttons at first.

	Purple	Gold
Before	5 u	4 u
Change	- 1 u	+ 0.4 u
After	4 u	4.4 u

Number of purple buttons in percentage
= 100% + 25%
= 125%

125% = ¹²⁵₁₀₀ = ⁵₄

Number of purple buttons that Sam removed
= 20% x 5 u
= ²⁰₁₀₀ x 5 u 
= 1 u

Number of gold buttons that Sam increased 
= 10% x 4 u
= ¹⁰₁₀₀  x 4 u
= 0.4 u

Number of purple buttons in the end
= 5 u - 1 u
= 4 u

Number of gold buttons in the end
= 4 u + 0.4 u
= 4.4 u

Number of fewer purple buttons than gold buttons in the end
= 4.4 u - 4 u 
= 0.4 u 

0.4 u = 28

1 u = 28 ÷ 0.4 = 70

Number of gold buttons at first
= 4 u
= 4 x 70
= 280

Answer(s): 280