There are 25% more purple marbles than grey marbles in a bag. After Michael removed 40% of the purple marbles and increased the number of grey marbles by 20%, there are now 126 fewer purple marbles than grey marbles. Find the number of grey marbles at first.

	Purple	Grey
Before	5 u	4 u
Change	- 2 u	+ 0.8 u
After	3 u	4.8 u

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

125% = ¹²⁵₁₀₀ = ⁵₄

Number of purple marbles that Michael removed
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u 
= 2 u

Number of grey marbles that Michael increased 
= 20% x 4 u
= ²⁰₁₀₀  x 4 u
= 0.8 u

Number of purple marbles in the end
= 5 u - 2 u
= 3 u

Number of grey marbles in the end
= 4 u + 0.8 u
= 4.8 u

Number of fewer purple marbles than grey marbles in the end
= 4.8 u - 3 u 
= 1.8 u 

1.8 u = 126

1 u = 126 ÷ 1.8 = 70

Number of grey marbles at first
= 4 u
= 4 x 70
= 280

Answer(s): 280