PSLE
Gillian had a total of 243 purple and red beads. She used 27 purple beads and 20% of the red beads. After that, the ratio of the number of purple beads to red beads Gillian had was 7 : 4.

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

	Purple	Red	Total
Before	7 u + 27	5 u	12 u + 27
Change	- 27	- 1 u
After	7 u	4 u	11 u
Comparing purple beads and red beads in the end	7	4	11

(a)
20% = ²⁰₁₀₀ = ¹₅

Fraction of her red beads that Gillian used = ¹₅

Fraction of her red beads that Gillian was left with
= 1 - ¹₅
= ⁴₅

(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 = 5 u
Number of purple beads at first = 7 u + 27

Total number of beads at first
= 5 u + 7 u + 27
= 12 u + 27

12 u + 27 = 243
12 u = 243 - 27
12 u = 216

1 u = 216 ÷ 12 = 18

Number of red beads in the end = 4 u
Number of purple beads in the end = 7 u

Number of more purple beads than red beads that Gillian had in the end
= 7 u - 4 u
= 3 u
= 3 x 18
= 54

Answer(s): (a)⁴₅; (b) 54