PSLE
Irene had a total of 263 purple and silver beads. She used 23 purple beads and 90% of the silver beads. After that, the ratio of the number of purple beads to silver beads Irene had was 6 : 1.

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

	Purple	Silver	Total
Before	6 u + 23	10 u	16 u + 23
Change	- 23	- 9 u
After	6 u	1 u	7 u
Comparing purple beads and silver beads in the end	6	1	7

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her silver beads that Irene used = ⁹₁₀

Fraction of her silver beads that Irene was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of silver 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 silver beads at first = 10 u
Number of purple beads at first = 6 u + 23

Total number of beads at first
= 10 u + 6 u + 23
= 16 u + 23

16 u + 23 = 263
16 u = 263 - 23
16 u = 240

1 u = 240 ÷ 16 = 15

Number of silver beads in the end = 1 u
Number of purple beads in the end = 6 u

Number of more purple beads than silver beads that Irene had in the end
= 6 u - 1 u
= 5 u
= 5 x 15
= 75

Answer(s): (a)¹₁₀; (b) 75