PSLE
Lynn had a total of 173 gold and black beads. She used 13 gold beads and 80% of the black beads. After that, the ratio of the number of gold beads to black beads Lynn had was 5 : 1.

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

	Gold	Black	Total
Before	5 u + 13	5 u	10 u + 13
Change	- 13	- 4 u
After	5 u	1 u	6 u
Comparing gold beads and black beads in the end	5	1	6

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

Fraction of her black beads that Lynn used = ⁴₅

Fraction of her black beads that Lynn was left with
= 1 - ⁴₅
= ¹₅

(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 = 5 u
Number of gold beads at first = 5 u + 13

Total number of beads at first
= 5 u + 5 u + 13
= 10 u + 13

10 u + 13 = 173
10 u = 173 - 13
10 u = 160

1 u = 160 ÷ 10 = 16

Number of black beads in the end = 1 u
Number of gold beads in the end = 5 u

Number of more gold beads than black beads that Lynn had in the end
= 5 u - 1 u
= 4 u
= 4 x 16
= 64

Answer(s): (a)¹₅; (b) 64