There are 10% as many gold marbles as grey marbles in Risa's collection of marbles. The number of yellow marbles is 35% fewer than the number of grey marbles. There are 451 more yellow marbles than gold marbles.

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

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

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

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

11 u = 451

1 u = 451 ÷ 11 = 41

Total number of marbles in the collection
= 2 u + 20 u + 13 u 
= 35 u
= 35 x 41
= 1435

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

Answer(s): (a) 1435; (b) 153¹¹₁₃ %