PSLE
Gwen had a total of 120 black and red beads. She used 12 black beads and 25% of the red beads. After that, the ratio of the number of black beads to red beads Gwen had was 8 : 3.

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

	Black beads	Red beads	Total
Before	8 u + 12	4 u	12 u + 12
Change	- 12	- 1 u
After	8 u	3 u	11 u
Comparing black beads and red beads in the end	8	3	11

(a)
25% = ²⁵₁₀₀ = ¹₄

Fraction of her red beads that Gwen used = ¹₄

(b)
The number of red 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 red beads at first = 4 u
Number of black beads at first = 8 u + 12

Total number of beads at first
= 4 u + 8 u + 12
= 12 u + 12

12 u + 12 = 120
12 u = 120 - 12
12 u = 108

1 u = 108 ÷ 12 = 9

Number of red beads in the end = 3 u
Number of black beads in the end = 8 u

Total number of beads in the end
= 8 u + 3 u
= 11 u
= 11 x 9
= 99

Answer(s): (a)¹₄; (b) 99