There are 10% as many purple marbles as white marbles in Abi's collection of marbles. The number of red marbles is 40% fewer than the number of white marbles. There are 255 more red marbles than purple marbles.

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

Purple	White	Red
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of white marbles is the repeated identity. Make the number of white marbles the same.  LCM of 10 and 5 is 10.

Number of more red marbles than purple marbles
= 6 u - 1 u
= 5 u

5 u = 255

1 u = 255 ÷ 5 = 51

Total number of marbles in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 51
= 867

(b)
Percentage of the number of white marbles as compared to the number of red marbles
= ⁵₃ x 100%
= ⁵⁰⁰₃ %
= 166²₃ %

Answer(s): (a) 867; (b) 166²₃ %