PSLE
Hazel had a total of 124 black and gold beads. She used 28 black beads and 90% of the gold beads. After that, the ratio of the number of black beads to gold beads Hazel had was 6 : 1.

1. What fraction of her gold beads was Hazel left with? Give your answer in the simplest form.
2. How many more black beads than gold beads did Hazel have in the end?

	Black	Gold	Total
Before	6 u + 28	10 u	16 u + 28
Change	- 28	- 9 u
After	6 u	1 u	7 u
Comparing black beads and gold beads in the end	6	1	7

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her gold beads that Hazel used = ⁹₁₀

Fraction of her gold beads that Hazel was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of gold 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 gold beads at first = 10 u
Number of black beads at first = 6 u + 28

Total number of beads at first
= 10 u + 6 u + 28
= 16 u + 28

16 u + 28 = 124
16 u = 124 - 28
16 u = 96

1 u = 96 ÷ 16 = 6

Number of gold beads in the end = 1 u
Number of black beads in the end = 6 u

Number of more black beads than gold beads that Hazel had in the end
= 6 u - 1 u
= 5 u
= 5 x 6
= 30

Answer(s): (a)¹₁₀; (b) 30