PSLE
Rachel had a total of 137 pink and purple beads. She used 46 pink beads and 40% of the purple beads. After that, the ratio of the number of pink beads to purple beads Rachel had was 2 : 3.

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

	Pink beads	Purple beads	Total
Before	2 u + 46	5 u	7 u + 46
Change	- 46	- 2 u
After	2 u	3 u	5 u
Comparing pink beads and purple beads in the end	2	3	5

(a)
40% = ⁴⁰₁₀₀ = ²₅

Fraction of her purple beads that Rachel used = ²₅

(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 = 5 u
Number of pink beads at first = 2 u + 46

Total number of beads at first
= 5 u + 2 u + 46
= 7 u + 46

7 u + 46 = 137
7 u = 137 - 46
7 u = 91

1 u = 91 ÷ 7 = 13

Number of purple beads in the end = 3 u
Number of pink beads in the end = 2 u

Total number of beads in the end
= 2 u + 3 u
= 5 u
= 5 x 13
= 65

Answer(s): (a)²₅; (b) 65