PSLE
Diana had a total of 216 pink and purple beads. She used 12 pink beads and 80% of the purple beads. After that, the ratio of the number of pink beads to purple beads Diana had was 7 : 1.

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

	Pink	Purple	Total
Before	7 u + 12	5 u	12 u + 12
Change	- 12	- 4 u
After	7 u	1 u	8 u
Comparing pink beads and purple beads in the end	7	1	8

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

Fraction of her purple beads that Diana used = ⁴₅

Fraction of her purple beads that Diana 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 pink beads at first = 7 u + 12

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

12 u + 12 = 216
12 u = 216 - 12
12 u = 204

1 u = 204 ÷ 12 = 17

Number of purple beads in the end = 1 u
Number of pink beads in the end = 7 u

Number of more pink beads than purple beads that Diana had in the end
= 7 u - 1 u
= 6 u
= 6 x 17
= 102

Answer(s): (a)¹₅; (b) 102