PSLE
Jean had a total of 159 green and purple beads. She used 19 green beads and 80% of the purple beads. After that, the ratio of the number of green beads to purple beads Jean had was 5 : 1.

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

	Green	Purple	Total
Before	5 u + 19	5 u	10 u + 19
Change	- 19	- 4 u
After	5 u	1 u	6 u
Comparing green beads and purple beads in the end	5	1	6

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

Fraction of her purple beads that Jean used = ⁴₅

Fraction of her purple beads that Jean was left with
= 1 - ⁴₅
= ¹₅

(b)
The number of purple 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 purple beads at first = 5 u
Number of green beads at first = 5 u + 19

Total number of beads at first
= 5 u + 5 u + 19
= 10 u + 19

10 u + 19 = 159
10 u = 159 - 19
10 u = 140

1 u = 140 ÷ 10 = 14

Number of purple beads in the end = 1 u
Number of green beads in the end = 5 u

Number of more green beads than purple beads that Jean had in the end
= 5 u - 1 u
= 4 u
= 4 x 14
= 56

Answer(s): (a)¹₅; (b) 56