There are 10% as many purple marbles as yellow marbles in Barbara's collection of marbles. The number of gold marbles is 35% fewer than the number of yellow marbles. There are 308 more gold marbles than purple marbles.

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

Purple	Yellow	Gold
1x2	10x2
	20x1	13x1
2 u	20 u	13 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

The number of yellow marbles is the repeated identity. Make the number of yellow marbles the same.  LCM of 10 and 20 is 20.

Number of more gold marbles than purple marbles
= 13 u - 2 u
= 11 u

11 u = 308

1 u = 308 ÷ 11 = 28

Total number of marbles in the collection
= 2 u + 20 u + 13 u 
= 35 u
= 35 x 28
= 980

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

Answer(s): (a) 980; (b) 153¹¹₁₃ %