PSLE
Jean had a total of 103 black and purple beads. She used 19 black beads and 10% of the purple beads. After that, the ratio of the number of black beads to purple beads Jean had was 4 : 9.

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

	Black beads	Purple beads	Total
Before	4 u + 19	10 u	14 u + 19
Change	- 19	- 1 u
After	4 u	9 u	13 u
Comparing black beads and purple beads in the end	4	9	13

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

Fraction of her purple beads that Jean used = ¹₁₀

(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 = 10 u
Number of black beads at first = 4 u + 19

Total number of beads at first
= 10 u + 4 u + 19
= 14 u + 19

14 u + 19 = 103
14 u = 103 - 19
14 u = 84

1 u = 84 ÷ 14 = 6

Number of purple beads in the end = 9 u
Number of black beads in the end = 4 u

Total number of beads in the end
= 4 u + 9 u
= 13 u
= 13 x 6
= 78

Answer(s): (a)¹₁₀; (b) 78