PSLE
Olivia had a total of 217 silver and purple beads. She used 49 silver beads and 40% of the purple beads. After that, the ratio of the number of silver beads to purple beads Olivia had was 7 : 3.

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

	Silver	Purple	Total
Before	7 u + 49	5 u	12 u + 49
Change	- 49	- 2 u
After	7 u	3 u	10 u
Comparing silver beads and purple beads in the end	7	3	10

(a)
40% = ⁴⁰₁₀₀ = ²₅

Fraction of her purple beads that Olivia used = ²₅

Fraction of her purple beads that Olivia was left with
= 1 - ²₅
= ³₅

(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 silver beads at first = 7 u + 49

Total number of beads at first
= 5 u + 7 u + 49
= 12 u + 49

12 u + 49 = 217
12 u = 217 - 49
12 u = 168

1 u = 168 ÷ 12 = 14

Number of purple beads in the end = 3 u
Number of silver beads in the end = 7 u

Number of more silver beads than purple beads that Olivia had in the end
= 7 u - 3 u
= 4 u
= 4 x 14
= 56

Answer(s): (a)³₅; (b) 56