PSLE
Olivia had a total of 186 purple and blue beads. She used 21 purple beads and 25% of the blue beads. After that, the ratio of the number of purple beads to blue beads Olivia had was 7 : 3.

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

	Purple	Blue	Total
Before	7 u + 21	4 u	11 u + 21
Change	- 21	- 1 u
After	7 u	3 u	10 u
Comparing purple beads and blue beads in the end	7	3	10

(a)
25% = ²⁵₁₀₀ = ¹₄

Fraction of her blue beads that Olivia used = ¹₄

Fraction of her blue beads that Olivia was left with
= 1 - ¹₄
= ³₄

(b)
The number of blue 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 blue beads at first = 4 u
Number of purple beads at first = 7 u + 21

Total number of beads at first
= 4 u + 7 u + 21
= 11 u + 21

11 u + 21 = 186
11 u = 186 - 21
11 u = 165

1 u = 165 ÷ 11 = 15

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

Number of more purple beads than blue beads that Olivia had in the end
= 7 u - 3 u
= 4 u
= 4 x 15
= 60

Answer(s): (a)³₄; (b) 60