There are 20% as many purple beads as red beads in Marion's collection of beads. The number of green beads is 30% fewer than the number of red beads. There are 350 more green beads than purple beads.

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

Purple	Red	Green
1x2	5x2
	10x1	7x1
2 u	10 u	7 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

The number of red beads is the repeated identity. Make the number of red beads the same.  LCM of 5 and 10 is 10.

Number of more green beads than purple beads
= 7 u - 2 u
= 5 u

5 u = 350

1 u = 350 ÷ 5 = 70

Total number of beads in the collection
= 2 u + 10 u + 7 u 
= 19 u
= 19 x 70
= 1330

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

Answer(s): (a) 1330; (b) 142⁶₇ %