PSLE
Raeann had a total of 169 gold and black beads. She used 49 gold beads and 50% of the black beads. After that, the ratio of the number of gold beads to black beads Raeann had was 10 : 1.

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

	Gold beads	Black beads	Total
Before	10 u + 49	2 u	12 u + 49
Change	- 49	- 1 u
After	10 u	1 u	11 u
Comparing gold beads and black beads in the end	10	1	11

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her black beads that Raeann used = ¹₂

(b)
The number of black 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 black beads at first = 2 u
Number of gold beads at first = 10 u + 49

Total number of beads at first
= 2 u + 10 u + 49
= 12 u + 49

12 u + 49 = 169
12 u = 169 - 49
12 u = 120

1 u = 120 ÷ 12 = 10

Number of black beads in the end = 1 u
Number of gold beads in the end = 10 u

Total number of beads in the end
= 10 u + 1 u
= 11 u
= 11 x 10
= 110

Answer(s): (a)¹₂; (b) 110