PSLE
Penelope had a total of 130 purple and silver beads. She used 10 purple beads and 75% of the silver beads. After that, the ratio of the number of purple beads to silver beads Penelope had was 6 : 1.

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

	Purple	Silver	Total
Before	6 u + 10	4 u	10 u + 10
Change	- 10	- 3 u
After	6 u	1 u	7 u
Comparing purple beads and silver beads in the end	6	1	7

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her silver beads that Penelope used = ³₄

Fraction of her silver beads that Penelope was left with
= 1 - ³₄
= ¹₄

(b)
The number of silver 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 silver beads at first = 4 u
Number of purple beads at first = 6 u + 10

Total number of beads at first
= 4 u + 6 u + 10
= 10 u + 10

10 u + 10 = 130
10 u = 130 - 10
10 u = 120

1 u = 120 ÷ 10 = 12

Number of silver beads in the end = 1 u
Number of purple beads in the end = 6 u

Number of more purple beads than silver beads that Penelope had in the end
= 6 u - 1 u
= 5 u
= 5 x 12
= 60

Answer(s): (a)¹₄; (b) 60