There are 25% as many black beads as purple beads in Shiyun's collection of beads. The number of blue beads is 30% fewer than the number of purple beads. There are 513 more blue beads than black beads.

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

Black	Purple	Blue
1x5	4x5
	10x2	7x2
5 u	20 u	14 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

The number of purple beads is the repeated identity. Make the number of purple beads the same.  LCM of 4 and 10 is 20.

Number of more blue beads than black beads
= 14 u - 5 u
= 9 u

9 u = 513

1 u = 513 ÷ 9 = 57

Total number of beads in the collection
= 5 u + 20 u + 14 u 
= 39 u
= 39 x 57
= 2223

(b)
Percentage of the number of purple beads as compared to the number of blue beads
= ¹⁰₇ x 100%
= ¹⁰⁰⁰₇ %
= 142⁶₇ %

Answer(s): (a) 2223; (b) 142⁶₇ %