There are 20% as many purple beads as pink beads in Olivia's collection of beads. The number of red beads is 35% fewer than the number of pink beads. There are 261 more red beads than purple beads.

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

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

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

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

9 u = 261

1 u = 261 ÷ 9 = 29

Total number of beads in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 29
= 1073

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

Answer(s): (a) 1073; (b) 153¹¹₁₃ %