PSLE
Yoko had a total of 165 black and purple beads. She used 12 black beads and 50% of the purple beads. After that, the ratio of the number of black beads to purple beads Yoko had was 7 : 1.

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

	Black	Purple	Total
Before	7 u + 12	2 u	9 u + 12
Change	- 12	- 1 u
After	7 u	1 u	8 u
Comparing black beads and purple beads in the end	7	1	8

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her purple beads that Yoko used = ¹₂

Fraction of her purple beads that Yoko 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 black beads at first = 7 u + 12

Total number of beads at first
= 2 u + 7 u + 12
= 9 u + 12

9 u + 12 = 165
9 u = 165 - 12
9 u = 153

1 u = 153 ÷ 9 = 17

Number of purple beads in the end = 1 u
Number of black beads in the end = 7 u

Number of more black beads than purple beads that Yoko had in the end
= 7 u - 1 u
= 6 u
= 6 x 17
= 102

Answer(s): (a)¹₂; (b) 102