There are 10% as many white marbles as yellow marbles in Kylie's collection of marbles. The number of silver marbles is 45% fewer than the number of yellow marbles. There are 378 more silver marbles than white 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 silver marbles? Leave your answer as a mixed number in its simplest form.

White	Yellow	Silver
1x2	10x2
	20x1	11x1
2 u	20 u	11 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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 silver marbles than white marbles
= 11 u - 2 u
= 9 u

9 u = 378

1 u = 378 ÷ 9 = 42

Total number of marbles in the collection
= 2 u + 20 u + 11 u 
= 33 u
= 33 x 42
= 1386

(b)
Percentage of the number of yellow marbles as compared to the number of silver marbles
= ²⁰₁₁ x 100%
= ²⁰⁰⁰₁₁ %
= 181⁹₁₁ %

Answer(s): (a) 1386; (b) 181⁹₁₁ %