PSLE
Gem had a total of 169 red and silver beads. She used 29 red beads and 90% of the silver beads. After that, the ratio of the number of red beads to silver beads Gem had was 4 : 1.

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

	Red	Silver	Total
Before	4 u + 29	10 u	14 u + 29
Change	- 29	- 9 u
After	4 u	1 u	5 u
Comparing red beads and silver beads in the end	4	1	5

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her silver beads that Gem used = ⁹₁₀

Fraction of her silver beads that Gem 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 red beads at first = 4 u + 29

Total number of beads at first
= 10 u + 4 u + 29
= 14 u + 29

14 u + 29 = 169
14 u = 169 - 29
14 u = 140

1 u = 140 ÷ 14 = 10

Number of silver beads in the end = 1 u
Number of red beads in the end = 4 u

Number of more red beads than silver beads that Gem had in the end
= 4 u - 1 u
= 3 u
= 3 x 10
= 30

Answer(s): (a)¹₁₀; (b) 30