There are 20% as many pink beads as gold beads in Risa's collection of beads. The number of purple beads is 35% fewer than the number of gold beads. There are 270 more purple beads than pink beads.

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

Pink	Gold	Purple
1x4	5x4
	20x1	13x1
4 u	20 u	13 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

The number of gold beads is the repeated identity. Make the number of gold beads the same.  LCM of 5 and 20 is 20.

Number of more purple beads than pink beads
= 13 u - 4 u
= 9 u

9 u = 270

1 u = 270 ÷ 9 = 30

Total number of beads in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 30
= 1110

(b)
Percentage of the number of gold beads as compared to the number of purple beads
= ²⁰₁₃ x 100%
= ²⁰⁰⁰₁₃ %
= 153¹¹₁₃ %

Answer(s): (a) 1110; (b) 153¹¹₁₃ %