PSLE
Barbara had a total of 131 orange and purple beads. She used 32 orange beads and 50% of the purple beads. After that, the ratio of the number of orange beads to purple beads Barbara had was 7 : 1.

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

	Orange	Purple	Total
Before	7 u + 32	2 u	9 u + 32
Change	- 32	- 1 u
After	7 u	1 u	8 u
Comparing orange beads and purple beads in the end	7	1	8

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her purple beads that Barbara used = ¹₂

Fraction of her purple beads that Barbara 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 orange beads at first = 7 u + 32

Total number of beads at first
= 2 u + 7 u + 32
= 9 u + 32

9 u + 32 = 131
9 u = 131 - 32
9 u = 99

1 u = 99 ÷ 9 = 11

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

Number of more orange beads than purple beads that Barbara had in the end
= 7 u - 1 u
= 6 u
= 6 x 11
= 66

Answer(s): (a)¹₂; (b) 66