PSLE
Winnie had a total of 126 purple and orange beads. She used 48 purple beads and 75% of the orange beads. After that, the ratio of the number of purple beads to orange beads Winnie had was 9 : 1.

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

	Purple	Orange	Total
Before	9 u + 48	4 u	13 u + 48
Change	- 48	- 3 u
After	9 u	1 u	10 u
Comparing purple beads and orange beads in the end	9	1	10

(a)
75% = ⁷⁵₁₀₀ = ³₄

Fraction of her orange beads that Winnie used = ³₄

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

(b)
The number of orange 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 orange beads at first = 4 u
Number of purple beads at first = 9 u + 48

Total number of beads at first
= 4 u + 9 u + 48
= 13 u + 48

13 u + 48 = 126
13 u = 126 - 48
13 u = 78

1 u = 78 ÷ 13 = 6

Number of orange beads in the end = 1 u
Number of purple beads in the end = 9 u

Number of more purple beads than orange beads that Winnie had in the end
= 9 u - 1 u
= 8 u
= 8 x 6
= 48

Answer(s): (a)¹₄; (b) 48