PSLE
Julie had a total of 169 red and black beads. She used 13 red beads and 75% of the black beads. After that, the ratio of the number of red beads to black beads Julie had was 8 : 1.

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

	Red beads	Black beads	Total
Before	8 u + 13	4 u	12 u + 13
Change	- 13	- 3 u
After	8 u	1 u	9 u
Comparing red beads and black beads in the end	8	1	9

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her black beads that Julie used = ³₄

(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 = 4 u
Number of red beads at first = 8 u + 13

Total number of beads at first
= 4 u + 8 u + 13
= 12 u + 13

12 u + 13 = 169
12 u = 169 - 13
12 u = 156

1 u = 156 ÷ 12 = 13

Number of black beads in the end = 1 u
Number of red beads in the end = 8 u

Total number of beads in the end
= 8 u + 1 u
= 9 u
= 9 x 13
= 117

Answer(s): (a)³₄; (b) 117