There are 25% as many pink marbles as purple marbles in Jane's collection of marbles. The number of grey marbles is 40% fewer than the number of purple marbles. There are 385 more grey marbles than pink marbles.

1. Find the total number of marbles in the collection.
2. What percentage are the number of purple marbles as compared to the number of grey marbles? Leave your answer as a mixed number in its simplest form.

Pink	Purple	Grey
1x5	4x5
	5x4	3x4
5 u	20 u	12 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of purple marbles is the repeated identity. Make the number of purple marbles the same.  LCM of 4 and 5 is 20.

Number of more grey marbles than pink marbles
= 12 u - 5 u
= 7 u

7 u = 385

1 u = 385 ÷ 7 = 55

Total number of marbles in the collection
= 5 u + 20 u + 12 u 
= 37 u
= 37 x 55
= 2035

(b)
Percentage of the number of purple marbles as compared to the number of grey marbles
= ⁵₃ x 100%
= ⁵⁰⁰₃ %
= 166²₃ %

Answer(s): (a) 2035; (b) 166²₃ %