PSLE
Winnie had a total of 271 gold and silver beads. She used 31 gold beads and 90% of the silver beads. After that, the ratio of the number of gold beads to silver beads Winnie had was 6 : 1.

1. What fraction of her silver beads was Winnie left with? Give your answer in the simplest form.
2. How many more gold beads than silver beads did Winnie have in the end?

	Gold	Silver	Total
Before	6 u + 31	10 u	16 u + 31
Change	- 31	- 9 u
After	6 u	1 u	7 u
Comparing gold beads and silver beads in the end	6	1	7

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her silver beads that Winnie used = ⁹₁₀

Fraction of her silver beads that Winnie was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of silver beads in the end is repeated.
Since the numbers are already the same, we do not need to use LCM to make them the same.

Number of silver beads at first = 10 u
Number of gold beads at first = 6 u + 31

Total number of beads at first
= 10 u + 6 u + 31
= 16 u + 31

16 u + 31 = 271
16 u = 271 - 31
16 u = 240

1 u = 240 ÷ 16 = 15

Number of silver beads in the end = 1 u
Number of gold beads in the end = 6 u

Number of more gold beads than silver beads that Winnie had in the end
= 6 u - 1 u
= 5 u
= 5 x 15
= 75

Answer(s): (a)¹₁₀; (b) 75