PSLE
Abi had a total of 159 gold and purple beads. She used 15 gold beads and 25% of the purple beads. After that, the ratio of the number of gold beads to purple beads Abi had was 8 : 3.

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

	Gold	Purple	Total
Before	8 u + 15	4 u	12 u + 15
Change	- 15	- 1 u
After	8 u	3 u	11 u
Comparing gold beads and purple beads in the end	8	3	11

(a)
25% = ²⁵₁₀₀ = ¹₄

Fraction of her purple beads that Abi used = ¹₄

Fraction of her purple beads that Abi was left with
= 1 - ¹₄
= ³₄

(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 = 4 u
Number of gold beads at first = 8 u + 15

Total number of beads at first
= 4 u + 8 u + 15
= 12 u + 15

12 u + 15 = 159
12 u = 159 - 15
12 u = 144

1 u = 144 ÷ 12 = 12

Number of purple beads in the end = 3 u
Number of gold beads in the end = 8 u

Number of more gold beads than purple beads that Abi had in the end
= 8 u - 3 u
= 5 u
= 5 x 12
= 60

Answer(s): (a)³₄; (b) 60