PSLE
Gabby had a total of 130 silver and purple beads. She used 30 silver beads and 50% of the purple beads. After that, the ratio of the number of silver beads to purple beads Gabby had was 8 : 1.

1. What fraction of her purple beads did Gabby use? Give your answer in the simplest form.
2. How many beads did Gabby have in the end?

	Silver beads	Purple beads	Total
Before	8 u + 30	2 u	10 u + 30
Change	- 30	- 1 u
After	8 u	1 u	9 u
Comparing silver beads and purple beads in the end	8	1	9

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her purple beads that Gabby used = 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 silver beads at first = 8 u + 30

Total number of beads at first
= 2 u + 8 u + 30
= 10 u + 30

10 u + 30 = 130
10 u = 130 - 30
10 u = 100

1 u = 100 ÷ 10 = 10

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

Total number of beads in the end
= 8 u + 1 u
= 9 u
= 9 x 10
= 90

Answer(s): (a)¹₂; (b) 90