PSLE
Jade had a total of 202 purple and silver beads. She used 37 purple beads and 50% of the silver beads. After that, the ratio of the number of purple beads to silver beads Jade had was 9 : 1.

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

	Purple	Silver	Total
Before	9 u + 37	2 u	11 u + 37
Change	- 37	- 1 u
After	9 u	1 u	10 u
Comparing purple beads and silver beads in the end	9	1	10

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her silver beads that Jade used = ¹₂

Fraction of her silver beads that Jade was left with
= 1 - ¹₂
= ¹₂

(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 = 2 u
Number of purple beads at first = 9 u + 37

Total number of beads at first
= 2 u + 9 u + 37
= 11 u + 37

11 u + 37 = 202
11 u = 202 - 37
11 u = 165

1 u = 165 ÷ 11 = 15

Number of silver beads in the end = 1 u
Number of purple beads in the end = 9 u

Number of more purple beads than silver beads that Jade had in the end
= 9 u - 1 u
= 8 u
= 8 x 15
= 120

Answer(s): (a)¹₂; (b) 120