There are 25% as many white marbles as purple marbles in Tina's collection of marbles. The number of pink marbles is 45% fewer than the number of purple marbles. There are 342 more pink marbles than white 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 pink marbles? Leave your answer as a mixed number in its simplest form.

White	Purple	Pink
1x5	4x5
	20x1	11x1
5 u	20 u	11 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

Number of more pink marbles than white marbles
= 11 u - 5 u
= 6 u

6 u = 342

1 u = 342 ÷ 6 = 57

Total number of marbles in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 57
= 2052

(b)
Percentage of the number of purple marbles as compared to the number of pink marbles
= ²⁰₁₁ x 100%
= ²⁰⁰⁰₁₁ %
= 181⁹₁₁ %

Answer(s): (a) 2052; (b) 181⁹₁₁ %