PSLE
Winnie had a total of 77 purple and blue beads. She used 17 purple beads and 75% of the blue beads. After that, the ratio of the number of purple beads to blue beads Winnie had was 8 : 1.

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

	Purple	Blue	Total
Before	8 u + 17	4 u	12 u + 17
Change	- 17	- 3 u
After	8 u	1 u	9 u
Comparing purple beads and blue beads in the end	8	1	9

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her blue beads that Winnie used = ³₄

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

(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 = 8 u + 17

Total number of beads at first
= 4 u + 8 u + 17
= 12 u + 17

12 u + 17 = 77
12 u = 77 - 17
12 u = 60

1 u = 60 ÷ 12 = 5

Number of blue beads in the end = 1 u
Number of purple beads in the end = 8 u

Number of more purple beads than blue beads that Winnie had in the end
= 8 u - 1 u
= 7 u
= 7 x 5
= 35

Answer(s): (a)¹₄; (b) 35