PSLE
Sarah had a total of 112 gold and purple beads. She used 22 gold beads and 50% of the purple beads. After that, the ratio of the number of gold beads to purple beads Sarah had was 8 : 1.

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

	Gold	Purple	Total
Before	8 u + 22	2 u	10 u + 22
Change	- 22	- 1 u
After	8 u	1 u	9 u
Comparing gold beads and purple beads in the end	8	1	9

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her purple beads that Sarah used = ¹₂

Fraction of her purple beads that Sarah was left with
= 1 - ¹₂
= ¹₂

(b)
The number of purple 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 purple beads at first = 2 u
Number of gold beads at first = 8 u + 22

Total number of beads at first
= 2 u + 8 u + 22
= 10 u + 22

10 u + 22 = 112
10 u = 112 - 22
10 u = 90

1 u = 90 ÷ 10 = 9

Number of purple beads in the end = 1 u
Number of gold beads in the end = 8 u

Number of more gold beads than purple beads that Sarah had in the end
= 8 u - 1 u
= 7 u
= 7 x 9
= 63

Answer(s): (a)¹₂; (b) 63