PSLE
Kathy had a total of 155 green and red beads. She used 23 green beads and 80% of the red beads. After that, the ratio of the number of green beads to red beads Kathy had was 6 : 1.

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

	Green	Red	Total
Before	6 u + 23	5 u	11 u + 23
Change	- 23	- 4 u
After	6 u	1 u	7 u
Comparing green beads and red beads in the end	6	1	7

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

Fraction of her red beads that Kathy used = ⁴₅

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

(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 green beads at first = 6 u + 23

Total number of beads at first
= 5 u + 6 u + 23
= 11 u + 23

11 u + 23 = 155
11 u = 155 - 23
11 u = 132

1 u = 132 ÷ 11 = 12

Number of red beads in the end = 1 u
Number of green beads in the end = 6 u

Number of more green beads than red beads that Kathy had in the end
= 6 u - 1 u
= 5 u
= 5 x 12
= 60

Answer(s): (a)¹₅; (b) 60